UC-NRLF 


SB    33 


NOTES  on  PRACTICA 


MECHANICAL 
DRA  WING 


UNIVERSITY  OF  CALIFORNIA. 


Class 


NOTES    ON 

PRACTICAL  MECHANICAL 
DRAWING 


WRITTEN    FOR    THE    USE    OF    STUDENTS 
IN    ENGINEERING    COURSES 


BY 


VICTOR    T.    WILSON,  M.  E. 

PROFESSOR  of  DRAWING  AND  DESIGN  at  the 

MICHIGAN  AGRICULTURAL  COLLEGE, 

EAST  LANSING,  MICHIGAN 


AND 


CARLOS  L.   McMASTER,   C.  E. 

ASSOCIATE  in  GENERAL  ENGINEERING  DRAWING 

at  the  UNIVERSITY  OF  ILLINOIS, 

URBANA,  ILLINOIS 


THIRD   EDITION 
EVISED  AND  ENLARGED 


PUBLISHED    BY 

WILSON  &  McMASTER,  EAST  LANSING,  MICHIGAN 
NINETEEN    HUNDRED   AND    NINE 


COPYRIGHT,  1909 

BY 
T.  WILSON  AND  C.  L.  MCMASTER 


RIPLEY  &  GRAY,  PRINTERS 
LANSING,  MICH. 


TH£ 

UNIVERSITY 

Of 


PREFACE 

This  book  is  a  collection  of  notes  intended  to  furnish 
the  basis  for  a  course  in  elementry  mechanical  drawing, 
so  arranged,  it  is  thought,  that  the  teacher  may  have  the 
widest  latitude  in  his  choice  of  sequence  of  subjects. 

Since  its  first  edition,  two  years  ago,  the  book  has 
been  rearranged  with  this  particular  point  in  view.  It  has 
been  thoroughly  revised  and  also  enlarged  by  the  addition 
of  more  explanatory  matter  and  illustrations  in  orthogra- 
phic projection,  by  a  chapter  upon  isometric  and  oblique 
drawing,  and  by  a  number  of  exercises  in  working  draw- 
ings from  sketches.  The  usual  geometrical  drawing  has 
been  reduced  to  a  minimum;  it  has  been  included,  not  for 
its  value  as  exercise  in  drawing,  but  for  the  knowledge 
conveyed  upon  constructive  processes  useful  in  the  science. 

Latest  practice  in  teaching  drawing  shows  the  influ- 
ence of  utilitarianism.  The  aim  of  a  mechanical  drawing 
is  to  record  useful  facts;  useful  facts,  therefore,  are  used 
as  exercises  from  the  beginning  of  the  study.  The  theo- 
retical or  geometrical  science  forms  but  a  very  small 
part  of  the  knowledge  required  in  the  subject  and,  where 
courses  in  drawing  are  necessarily  short,  the  maximum  of 
practical  information  is  aimed  at.  The  course  here  out- 
lined uses  working  drawings  as  exercises  almost  from  the 
very  beginning. 

Of  course,  the  actual  subject,  from  which  to  draw,  is 
most  to  be  desired,  but  it  is  not  always  available  or 
practicable,  particularly  in  the  beginning  and  with  large 


190876 


iv  PREFACE. 

classes,  therefore  numerous  working  drawing  sketches  are 
presented  as  problems.  Again,  nothing  can  take  the  place 
of  the  personal  guidance  of  the  teacher  in  inculcating  good 
methods  of  work,  but  large  classes  make  the  individual 
direction  by  the  teacher  difficult,  hence,  minute  directions 
are  given  upon  the  care  and  use  of  tools  and  methods  of 
working  to  aid  the  teacher  and  student.  And  it  may  be 
stated,  from  their  experience,  it  is  the  conviction  of  the 
authors,  that,  where  good  methods  and  system  in  working 
are  insisted  upon  from  the  beginning,  the  quality  of  the 
the  product  is  greatly  improved.  This  theory  is  opposed 
to  the  one  that  practice  only,  together  with  quantity, 
makes  perfect. 

Of  course  it  is  expecting  a  great  deal  of  the  student 
that  he  grasp  all  the  practical  points  given  in  a  short 
course,  but,  here  again,  experience  has  verified  the  con- 
viction that  it  is  possible  and  especially  where  the  exercises 
are  made  to  be  of  interest,  for  where  interest  is  aroused 
individual  initiative  will  do  the  rest. 

Quotations  have  here  and  there  been  made  from 
standard  works  on  drawing,  and  acknowledgment  has 
been  given  in  each  case. 

V.  T.  WILSON. 

C.    L.    McMASTEK. 


TABLE    OF    CONTENTS. 


CHAPTER    I. 
LETTERING. 

Kinds  of  letters  in  common  use.  Lettering  in  design.  Variations  in  width, 
height,  etc.  Stability  of  letters.  The  Roman  and  Gothic  capitals 
and  small  letters  and  numerals.  Off-hand  lettering.  The  Old  Roman 
and  Roman-Gothic  letters.  Titles.  Bills  of  materials—  ...1-18 


CHAPTER    II. 
ORTHOGRAPHIC    PROJECTION. 

Drawing  as  a  science.  Definition  of  projection,  and  the  coordinate  planes. 
The  two  planes  folded  one  upon  another,  forming  four  dihedral  angles. 
The  projections  of  a  point  discussed.  The  projections  of  a  limited 
line,  plain  figures  and  solids.  The  end  plane.  Any  oblique  plane  of 
projection.  The  circle  in  projection,  any  curve  in  general.  Dif- 
ference between  first  and  third  angle  projection.  Problems 19-38 

CHAPTER    III. 
ISOMETRIC    AND    OBLIQUE    DRAWING. 

Definition  of  isometric  drawing.  The  difference  between  isometric  draw- 
ing and  isometric  projection.  The  conditions  of  isometric  projection 
described.  The  treatment  of  curves.  Oblique  projection  described...89-43 

CHAPTER    IV. 
THE    USE    OF    INSTRUMENTS. 

Practical  points  about  drawing  materials  and  instruments.  Peculiarities 
of  tracing  cloth.  Stretching  of  paper.  Drafting  machines.  Care  and 
handling  of  tools.  Use  of  each  tool  for  its  proper  purpose  and  keeping 
them  handy.  Detailed  directions  in  use  of  ruling  pen,  how  to  avoid 
errors  with  and  how  to  sharpen.  Directions  for  penciling  drawings, 
and  care  of  pencil.  System  of  penciling.  Detailed  directions  for  ink- 
ing drawings,  character  of  lines  to  use.  System  of  inking.  Cleaning 
drawings.  Handling  compass,  dividers  and  bows.  Use  of  irregular 
curve ...  ...44-65 


V  TABLE   OF  CONTENTS. 

CHAPTER    V. 
WORKING    DRAWINGS. 

Orthographic  projection  and  working  drawings.  Of  what  a  set  of  working 
drawings  consists.  Violation  of  rules  of  orthographic  projection  in 
working  drawings.  Development  and  arrangement  of  a  set  of  working 
drawings.  Drawing  to  scale,  and  directions  in  the  use  of.  Sections. 
Standard  section  lining.  Some  practical  hints.  Rules  of  projection 
violated  in  sections.  Dimensioning.  Practical  hints  in  dimensioning. 
Dimensioning  of  certain  features.  Notes  for  finish.  Markings  on 
drawings.  Checking.  Conventions  in  common  use.  Tracings.  V  and 
square  threaded  screws  analyzed.  Peculiarities  of  the  curve.  The  V 
threaded  screw.  The  conventionalization  for  threads.  The  Whitworth 
standard.  The  U.  S.  standard.  Other  forms  of  thread.  The  hexagonal 
form  of  bolt  heads  Names  of  various  bolts  and  screws.  Rivets. 
General  directions  for  the  treatment  of  problems.  Twenty- three 
miscellaneous  problems  in  working  drawings 66-152 

CHAPTER   VI. 
GEOMETRICAL    DRAWING. 

Geometrical  drawing  vs.  mechanical  drawing.  To  draw  a  tangent  to  an 
irregular  curve  at  a  point  on  the  curve.  To  rectify  an  arc  of  a  curve 
or  of  a  circle  subtending  a  small  angle.  To  draw  an  arc  of  given  radius 
tangent  to  two  given  oblique  lines.  The  conies.  To  draw  an  ellipse  by 
the  focii  method,  by  the  method  of  the  trammel,  and  approximately 
with  the  compass.  To  draw  a  parabola  by  means  of  the  focus.  To 
draw  a  hyperbola  by  means  of  its  focii,  by  the  rectangle  method.  The 
cycloid.  To  construct  the  cycloid.  To  construct  the  epicycloid,  the 
hypocycloid.  To  draw  the  involute  of  a  circle.--  ...153- 172 


CHAPTER  VII. 
MACHINE  SKETCHING. 

Sketching  as  an  accomplishment  of  the  engineer.  Scale  in  sketching.  Pro- 
portion in  sketching.  The  problem  in  hasty  sketching.  Treatment 
and  arrangement  of  views.  Practical  points  about  sketching 178-177 

APPENDIX. 

Blue  print  process  and  reproduction 178-180 

INDEX 

...181-186 


NOTES  ON 
PRACTICAL  MECHANICAL  DRAWING. 


CHAPTER    I  . 
LETTERING.* 

1.  The  lettering,  which  the  draftsman,  in  practice,  uses 
most,  is  a  rapidly  executed  statement,  on  a  drawing,  in 
what  is  known  as  an  off-hand  style.    It  is  a  very  simple 
letter  which  he  learns,  with  practice,  to  do  in  ink  without 
any  preliminary  pencil  layout,  beyond  the  limiting  lines, 
to  show  the  height  of  the  letters. 

Before  the  beginner,  however,  can  hope  to  attain  a 
proficiency,  in  even  the  free  lettering  mentioned,  he  should 
study  carefully  letter  forms  as  they  have  been  gradually 
developed  through  the  centuries,  to  what  are  called 
standard  proportions. 

2.  Good  lettering  is  not  mechanical,  but  is  good  design. 

The  straight  edge,  compass  or  other  tools,  have  no  place 
in  the  drawing  of  letters,  beyond  the  making  of  the 
limiting  lines  just  mentioned.  Good  design  requires:  (a.) 
Simplicity  of  style,  instanced  in  the  advertisements  con- 
fronting us  so  commonly  every  day.  (b.)  Uniformity  of 

*The  matter  upon  lettering  is  extracted  from  "Free-hand  Lettering,"  by 
Victor  T.  Wilson,  by  kind  permission  of  the  publishers,  Messrs.  John  Wiley  & 
Sons. 


^  NOTES   ON   PRACTICAL  MECHANICAL  DRAWING. 

effect,  as  the  units  in  any  design  are  distributed  through- 
out the  area  to  be  covered.  The  letters,  that  is,  should 
appear  to  be  of  the  same  height,  the  same  general  size, 
and  the  spacing  should  also  appear,  to  be  uniform.  These 
things  can  only  be  properly  attained  through  judgment 
and  taste  combined  with  accuracy  of  eye  in  the  detection 
of  small  differences. 

3.  Letters  actually  vary  in  width,  because  those  which  do 
not  fill  their  rectangle  of  space,  as  the  H  does,  look  smaller 
if  they  are  made  of  the  same  width  as  the  H.    They  must 
be    made    slightly    wider   than   the    normal    letter;    for 
example,  the  letter  A  must  be  spread  at  the  base,  because 
it  only  occupies  half  the  rectangle  of  space  allotted  to  it; 
likewise  the  B,  C,  D,  etc.,  must  be  widened,  each  to  a  dif- 
ferent degree.    The  exceptions  to  this  are  the  L  and  the 
F,  which  are  made  narrower  than  the  normal  letter. 

4.  Letters   actually  vary   in   height,   because,   where   a 
letter  touches  its  upper  and  lower  limits  only  by  tangency, 
it  would  look  shorter  than  the  H  or  N,  if  made  tangent  to 
them;  it  must  be  made  to  slightly  exceed  both  limiting 
lines,  as  the  C,  Gr,  and  0.    Letters  such  as  A,  V,  etc., 
should  also  exceed  the  limits,  if  their  angles  are  made 
sharp;  to  overcome  this  they  are  often  somewhat  blunted. 

5.  Letters  are  modified  to  produce  an  effect  of  stability; 

that  is,  those  letters  that  have  upper  and  lower  parts,  dis- 
tinctly separated,  appear  more  stable,  and  of  good  form, 
if  the  lower  section  is  made  larger  than  the  upper;  for 
example,  the  lower  lobe  of  the  B,  the  spread  of  the  arms 


LETTERING.  3 

of  the  X,  the  K,  the  lower  horizontal  stroke  of  the  E  and 
the  Z;  the  lower  curve  of  the  S,  also,  is  made  larger  ac'ross 
and  higher  than  the  upper. 

6.  Letters  are  further  varied  in  their  several  variations; 

that  is,  when  combined  into  words,  slight  modifications 
can  be  introduced,  here  and  there,  to  advantage;  for 
example,  an  L,  just  preceeding  an  A,  can  be  made  nar- 
rower than  if  it  were  followed  by  an  H  or  were  at  the  end 
of  a  word  or  a  line.  To  mechanically  figure  out  all  these 
modifications  simply  spoils  the spontaniety  of  design;  they 
must  be  the  result  of  judgment  applied  in  each  particular 
case.  Hence,  the  student  should  not  regard  the  modifica- 
tions shown  on  the  plates  as  having  any  value,  beyond 
suggestions  to  aid  in  the  formation  of  correct  perceptions. 

7.  A   knowledge   of    free-hand   drawing   is   essential   to 

facility  in  lettering  because  the  eye  is  then  trained  to  see 
form  and  to  judge  of  effects;  moreover  lettering  should  be 
developed  much  as  a  free-hand  drawing  is  developed,  by 
first  getting  a  broad,  simple  effect  and  proceeding  to  the 
details  gradually  in  the  order  of  their  importance. 

8.  Figure   1   shows  the  upper  case  Roman  letter,   in   a 

standard  form.  Upper  and  lower  case  are  terms  used  by 
printers  for  capital  and  small  letters,  so  named,  because 
the  type  representing  them  are  placed,  respectively,  in  the 
upper  and  lower  part  of  the  type  case. 

The  Roman  letter  has  no  really  standard  form,  in 
which  exact  proportioning  is  attainable.  The  ancestors  of 
this  letter  had  a  very  different  form  from  that  we  now  find 


NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 


1 


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LETTERING.  5 

in  the  printer's  type,  or  in  modern  good  examples.  It  has 
been  modified  and  changed  by  different  authorities,  we 
cannot  point  to  any  one  illustration  of  a  perfectly  correct 
Roman  type,  but  to  many,  varying  slightly  in  some  cases, 
quite  radically  in  others.  This  letter  is  a  refinement  of  an 
imitation  of  the  strokes  of  the  quill  used  by  the  early 
scribes.  It  is  nearly  square,  in  fact  was  square,  in  its 
early  forms. 

Eef erring  to  the  figure,  the  heavy  stems  are  made  a 
normal  width  of  one  unit,  the  height  of  the  letter  being 
divided  into  six  parts  called  units.  The  numerals  at  the 
bottom  of  each  letter  also  stand  for  units.  If  the  body  of 
a  letter  varies  in  thickness,  as  the  B,  C,  Gr,  etc.,  the  maxi- 
mum width,  at  the  middle,  is  slightly  greater  than  one 
unit,  the  S  and  U  being  exceptions. 

The  large  spurs  on  the  E,  F,  L,  T  and  Z  do  not  join 
the  body  of  the  letters  like  the  serifs,  by  tangent  curves; 
they  meet  the  horizontal  strokes  abruptly. 

The  mid-horizontal  strokes  of  the  B,  E,  F,  H  and  R 
are  put  slightly  above  the  center  of  the  space,  to  lend  an 
effect  of  stability,  the  P  is  an  exception  to  this. 

The  inner  and  outer  edges  of  the  curved  parts  of 
letters,  as  B,  C,  0,  P,  and  the  upper  part  of  the  letter  R, 
are  formed  by  arcs  of  regular  curves  with  vertical  and 
horizontal  axes;  the  inner  ones  approach  the  outer 
tangentially.  The  vertical  axes  of  the  outer  curves  are 
slightly  larger  than  their  horizontal  ones,  except  the  U. 

The  difficulties  of  drawing  the  S,  common  to  beginners, 
may  be  materially  lessened  by  using  an  O,  of  the  same 
proportions,  as  a  basis  in  sketching. 


NOTES   ON   PRACTICAL  MECHANICAL  DRAWING. 


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LETTERING.  7 

9.  The  small  letters  are  shown  in  Fig.  2,  to  harmonize 
with  the  capitals.  These  may  be  divided  into  three 
classes,  ascending,  descending  and  short  letters.  The 
ascending,  except  the  *t,7  have  a  height  equal  to  the  capitals, 
and  the  descending  are  the  same  in  total  length.  The 
height  of  the  short  letters,  relative  to  the  others,  is  not 
fixed,  but  they  generally  vary  between  about  one-half  and 
two-thirds  the  height  of  the  capitals.  In  the  figure  they 
are  six-tenths.  • 

The  width  and  height  of  the  small  letters  are  related 
to  each  other,  in  the  same  manner  as  the  corresponding 
dimensions  of  the  capitals.  The  height  of  the  short  letters 
is  divided  into  six  parts,  each  a  unit  for  both  the  width  of 
the  letter  and  the  weight  of  body.  The  same  peculiarities, 
as  to  variations,  which  occur  in  the  capitals,  also  occur  hi 
the  small  letters. 

FIGURE    No.    8 


1O.  The  Roman  numerals  are  shown  in  Fig.  3.  They 
can  be  made  the  height  of  the  capitals  or  slightly  shorter, 
according  to  taste.  They  have  the  same  peculiarities,  as 
to  variation  in  height,  width  and  weight  of  body,  that  the 
letters  do. 


NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 


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LETTERING.  9 

11.  The   Gothic   or  uniform  body  letter,   as    shown  in 
Fig.  4,  is  one  of  most  common  use  by  draftsmen,  either 
as    a   heavy   body    or    a    light    one    made   by  a    single 
stroke  of  the  pen.    For  a  letter  to  appear  as  heavy  as  the 
Roman,  the  Gothic  is  made  slightly  thinner  in  the  stems. 
Note  that  the  ends  of  all  letters  are  cut  off  perpendicularly 
to  the  outside  edge  of  the  body.    It  has  the  same  varia- 
tions as  noted  in  the  Roman. 

12.  Off-hand    lettering    is    shown    in    Fig.    5,    in    the 
simplest  and  probably  the  most  common  style,  the  Gothic. 
It  should  be  made  directly  with  the  pen,  the  limiting  lines 
only  being  ruled ;  this  last,  the  beginner  should  never  fail 
to  do. 

It  has  been  found  that  a  certain  system  in  strokes 
produces  the  best  results  and  such  an  analysis  is  given  in 
the  upper  rows,  showing  several  ways  of  doing  it,  any  one 
of  which  is  good.  It  requires  a  great  deal  of  skill  to 
handle  off-hand  lettering  satisfactorily,  and  the  beginner 
should  hot  be  discouraged  at  the  large  amount  of  practice 
work  necessary  to  attain  it. 

Cultivate  a  steady,  uniform  stroke,  as  far  as  possible, 
towards  the  person,  as  a  basis  for  these  letters.  It  is 
impracticable  to  depend  upon  patching  unsatisfactory 
lines. 

Rows  4  and  5,  of  Fig.  5,  are  the  same  letter  as  that  in 
the  first  three  rows,  and  is  of  a  standard  proportion  and 
quite  common  size.  Rows  6  and  7  are  the  same  letter 
inclined.  The  inclination  should  be  about  20°  from  the 
vertical ;  it  can  be  somewhat  greater,  but  it  should  not  be 
less,  else  it  is  apt  to  look  like  a  poor  attempt  at  the  vertical 


1U  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING 

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LETTERING.  11 

style.  An  important  point  to  note,  in  the  inclined  style,  is 
that  V  and  W,  etc.,  are  so  inclined  that  the  bisector  of 
the  angle  of  the  sides  has  the  direction  of  the  main  stems 
of  the  other  letters.  Also,  note  that  the  O  forms,  if  accur- 
ately made,  are  inscribable  in  a  parallelogram,  whose 
inclined  sides  have  the  direction  of  the  main  stems  of  the 
other  letters;  that  is,  the  axes  of  the  oval  forms  do  not 
have  exactly  this  direction. 

The  kind  of  pen  used  for  this  letter  will  determine 
the  weight  of  the  strokes.  At  first  it  will  be  found  difficult 
to  make  a  continuous  straight  stroke  of  uniform  weight ; 
to  aid  in  doing  this;  first,  hold  the  pen  so  that  the  plane  of 
the  pen  axis,  and  the  line  to  be  made,  are  perpendicular  to 
each  other,  then  touch  the  paper,  pressing  the  nibs  of  the 
pen  apart  to  the  proper  width  before  starting  the  stroke; 
after  starting,  continue  motion  uninterruptedly  until  the 
end,  and  lift  the  pen  just  an  instant  after  stopping  motion, 
else  the  line  will  taper  to  a  fine  point.  If  a  lump  accumu- 
lates upon  either  end  of  the  line,  it  can  be  overcome  by 
carrying  less  ink  in  the  pen,  combined  with  a  briefer  hesita- 
tion at  beginning  and  ending.  Whole  arm  motion  is  found 
helpful. 

Fig.  6  shows  some  other  styles  of  off-hand  lettering. 
Rows  1  and  2  are  based  upon  the  Gothic  and  have  its 
characteristics,  mainly,  while  rows  3  and  4  show  a  free 
style  appropriate  to  architectural  drawings.  The  propor- 
tions of  letters  used  depend  upon  the  space  allowable  for 
them;  however,  a  broad  letter  finds  more  favor  than  a 
narrow  one.  It  is  certain  that  increasing  the  breadth  of  a 
letter  increases  its  legibility  more  than  a  corresponding  and 
proportional  increase  in  height.  The  expanded  form  is 
shown  in  several  places  later  on. 


12  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 


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£> 

i 

1 

^ 

i 

•8 

^ 

§ 

§ 
=8 

^ 

(M 

M 

— 

— 

to 

LETTERING.  13 

13.  The   desirable   size  for   an   off-hand  letter   depends 
upon  circumstances;  if  it  is  made,  for  example,  from  one 
to  one  and  one-half  times  as  wide  as  it  is  high,  the  short 
letters  may  be  one-sixteenth  of  an  inch  in  height,  as  it 
is  made  narrower  the  height  must  be  increased,  for  equal 
legibility,  in  greater  proportion.    The  usual  sizes  may  be 
said  to  vary  between  one-sixteenth  and  one-eighth  of  an 
inch. 

14.  The  desirable  pen  to   use,  may  be  a   ball  pointed 
pen,  if  fine,  or  a  Gillott's  303;  the  latter  should  be  worn 
down  a  little  to  produce  the  most  satisfactory  results. 
The  falcon  pen  is  also  a  good  one;  any  pen  of  medium 
stiffness,  will  do  which  will  make  the  desired  weight  of 
stroke  without  patching.    In  wiping  the  pen,  be  careful  not 
to  press  the  nibs  too  far  apart  against  the  wiping  cloth, 
they  are  apt  to  take  a  set  and  spoil  the  spring  in  the  pen. 
In  filling  the  pen,  use  the  quill  attached  to  the  cork,  in 
preference  to  dipping  the  pen  in  the  bottle,  as  the  handle 
is  apt  to  get  ink  on  it.     Clean  the  pen  every  time  it  has  to 
be  filled  and  keep  the  ink  bottle  closed,  tight,  except  when 
filling  pen. 

15.  The  old  Roman  letter  is  shown  in  Fig.  7,  rows  1  to 
5.    It  is  an  attempt  to  preserve  as  much  as  possible  of  the 
early  type  of  the  Roman  as  is  consistent   with   modern 
requirements  in  letters.    It  is  a  beautiful  form  and  is 
increasing  in  popularity;  it  is  a  much  freer  letter  than  the 
conventional  Roman,  and,  being  free,  it  is  not  found  in 
such  a  uniform  style,  there  are  more  variations  indulged 
in.    The  letter  here  shown  is  a  very  careful  compilation 
from  the  best  authorities. 


14  NOTES  ON  PRACTICAL  MECHANICAL  DRAWING. 


u-O 


co         > 

.  CO  00 


-oQ 


o 


LETTERING.  15 

16.  The  Roman-Gothic  letter  is  shown  in  rows  6  and  7. 
It  is  a  very  popular  form  of  letter  today,  being  a  combina- 
tion of  two  styles,  as  its  name  implies.     It  probably  is 
preferred,  because  of  its  heavy  face  and  consequent  ease 
of  construction. 

17.  Titles  to  drawings  are  placed,  commonly,  in  the 
right-hand  lower  corner  and  consist  of  (a)  the  designation 
for  the  drawing,  (b)  the  firm  for  whom  it  is  made,  (c)  the 
scale,  (d)  the  date,  and  frequently  a  set  of  items  such  as 
'checked  by,'  'corrected,'  'traced  by,'  etc. 

In  designating  titles  to  drawings,  the  fundamental  re- 
quisite is  appropriateness;  simplicity  in  style  is  an  adjunct 
to  this  for  working  drawings,  and  the  simplest  letter  is 
the  Gothic. 

Titles  are  generally  made  wholly  in  capitals,  although 
there  is  no  rule  to  control  this.  If  small  letters  are  used, 
it  is,  generally,  where  minor  matter  has  to  be  compressed 
into  small  space. 

It  is  well  to  lay  out  the  whole  title  in  a  design  with  a 
very  simple  contour  shape,  and  give  a  suggestion  only  of 
the  weight  of  the  different  lines.  Find  the  middle  or  axial 
line,  of  the  title  and  sketch  in  on  both  sides  of  it.  Fig.  8 
shows  a  method  of  laying  out  a  simple  title. 

Make  minor  connectives  small  and,  if  short,  preferably 
use  an  expanded  letter.  The  title  should  look  equally 
well  if  all  connectives,  as  'made  by,'  'for,'  etc.,  are  left 
out. 

Use  only  a  few  styles  of  letters  in  a  title,  not  more 
than  three,  preferably  one,  and  do  not  depend  upon 


16  NOTES   ON   PRACTICAL  MECHANICAL  DRAWING. 

O 


L^J 


T3  ^ 
C   rO 
-L  .  D~ 


(O      U 


o£      Q 

mm. 


0 
CO 


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0 


Id  f  '   •  ,   0  b  a 
— I        •  111  5 

FT  «f  Vr  O:Q< 


< 


Q_    y 

z 
< 


o--o^Dl 

<£   r~~C   CLC  ir 


c 

£P  I  TJ  O 

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°  "S 


LJ  I-  *^  Ll  Q  u  CL 
-I  tf  Q.  I  P  Q'^ 


I          ^=^v  O 


CO 


CO 


LETTERING. 
FIGURE    No.  9. 


17 


PLAN  OF 

PROPOSED  EXTENSION 

of  the 

WATER  SUPPLY  SYSTEM 


of  the 


YOF  LAWRENCE 


^Showing  the  connections  with  existing  mains. 

Prepared  under  the  direction   of 

Chas.H.HiU  CityEng'r. 

1907 
•Scale  ^-»    Feet 


LOCATION  SURVEY 

PLAN  AND  PROFILE 


FDR  THE: 


Prepared       by      the 

Engineering    Department 

Nashville    —  Tenn. 
June  _K_  1908 
Scale  of  Feet 


18  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 

variety  of  treatment  but  upon  harmony,  neatness,  com- 
pactness and  legibility. 

The  two  titles  of  Fig.  9  illustrate  the  style  common  in 
civil  engineering  and  map  drawing.  More  painstaking 
work  is  characteristic  of  civil  engineering  practice  in 
lettering  than  is  found  in  other  professions.  The  second 
title  is  of  the  simplest  style.  The  first  is  more  difficult, 
being  the  Eoman  letter  throughout. 

18.  Combinations  of  Roman  and  stump  letters,  either 
verticle  or  inclined,  are  found  in  the  majority  of  titles  on 
maps    of    all    kinds,    including    municipal    maps.      The 
difficulty  of  construction  limits  its  field  to  the  higher  class 
of  finished  drawings.     The  letter  may  also  be  executed 
very  acceptably  off-hand.     Such  titles  are  very  common  in 
engineering  practice. 

The  stump  letter  is  shown  in  the  last  two  rows  on  Fig. 
5,  the  capitals,  for  which,  are  the  inclined  Roman. 

19.  A  bill  of  materials  is  often  attached  to  drawings. 
It  may  be  in  a  corner  of  the  sheet,  and  usually  the  lower 
right-hand  corner,  above  the  title  or  it  may  be  upon  a 
separate  sheet  or  sheets,  if  it  is  very  extended.    It  is  made 
in  off-hand  lettering,  neatly  executed.    Its  contents  will  be 
further  discussed  in  Chapter  IV.     The  lower  part  of  Fig. 
6  gives  examples  of  such  tabulation. 


CHAPTER    II. 
ORTHOGRAPHIC    PROJECTION. 

2O.  Drawing  is  the  art  or  science  of  recording  a  person's 
impressions  about  things  by  a  more  or  less  accurate  sug- 
gestion of  form.  It  is  a  technical  subject  of  great  value 
to  the  engineer  and  architect,  the  graphical  language  with 
which  they  work  and  by  which  they  convey  their  ideas  to 
those  who  construct  the  things  they  lay  out.  It  is  the 
language,  moreover,  understood  by  all  nations,  having  for 
its  purpose  the  complete  representation  of  any  object  or 
structure  to  be  erected. 

All  drawings  may  be  divided  into  two  general  classes. 
(a.)  The  drawings  of  objects  as  viewed  at  a  finite 
distance,  (b.)  The  drawings  of  objects  as  viewed  at  an 
infinite  distance.  The  first  of  these  is  called  perspective. 
The  point  of  view  at  a  finite  distance  is  called  the  center  of 
projection.  It  is  as  if  the  eye  were  at  the  point  and  the 
drawing  of  the  object  was  made  upon  a  transparent  plane 
placed  between  the  latter  and  the  center  of  projection,  that 
is,  projected  upon  it  from  this  center  by  lines  from  the 
center  passing  through  all  points  of  the  object.  It  is  a 
kind  of  drawing  that  is  found  in  pictures.  In  the  second 
class  the  center  of  projection  or  the  eye  is  theoretically 
moved  to  an  infinite  distance,  that  is,  the  projecting  lines, 
from  the  object  to  the  plane,  become  parallel.  This,  in  a 
certain  form  of  drawing,  is  what  is  called  orthographic 
projection. 


20  NOTES   ON   PRACTICAL  MECHANICAL  DRAWING. 

Things  are  constructed  and  manufactured  from  draw- 
ings made  according  to  the  principles  of  the  second  kind 
mentioned,  or  orthographic  projection.  They  may  be 
made  free-hand,  that  is  by  sketches,  or  they  may  be  made 
by  careful  mechanical  drawings. 

A  mechanical  drawing,  used  for  the  purpose  of  con- 
struction, then,  consists  of  one  or  more  views,  made 
according  to  the  principles  of  orthographic  projection;  in 
addition  to  which  the  sizes  of  parts  are  clearly  set  forth  by 
dimensions,  notes  or  other  symbols  that  are  required  to 
accurately  construct  the  same.  • 

No  matter  how  simple  is  the  subject  to  be  constructed, 
an  accurate  and  comprehensive  and  unmistakable  drawing 
should  be  made  of  it.  The  test  of  a  good  working  drawing 
lies  in  the  fact  that  the  workman  can  make  nothing  out  of 
the  facts  contained  thereon  than  what  was  intended  by  the 
draftsman.  The  entire  meaning  should  be  clear  beyond 
the  shadow  of  a  doubt.  To  choose  the  number  of  views 
that  this  may  be  attained,  to  put  on  the  dimensions  which 
the  workman  will  need  in  making  the  subject,  is  the 
problem  of  the  draftsman.  The  needs  of  the  workman 
should  be  constantly  in  his  mind. 

21.  Orthographic  projection  is  the  science  of  represent- 
ing forms  by  projecting  them  upon  two  or  more  planes  by 
means  of  projecting  lines  respectively  perpendicular  to 
these  planes. 

The  center  of  projection,  from  which  the  projecting 
lines  eminate,  is  infinitely  distant  in  a  direction  perpen- 
dicular to  the  planes  of  projection,  and,  since  they  pass 
through  a  common  point  at  infinity,  they  are  parallel. 


ORTHOGRAPHIC  PROJECTION. 


The  'coordinate  planes  of  projection,'9  is  a  term  used  to 
designate  the  three  fundamental  planes  in  common  use, 
namely,  a  vertical  plane  (V),  a  horizontal  plane  (H),  and 


FIGURE    No .  10. 


4th-  L 


p? 


a  plane  perpendicular  to  these  two,  known  as  the  end 
plane,  or  profile  plane  (E  or  P).  The  vertical  and  the 
horizontal  planes  intersect  each  other  in  a  line  known  as  a 
k ground  line1  (G.L.)  and  each  is  indefinite  in  extent. 

Fig.  10  shows  a  picture  as  in  perspective,  of  these 


22  NOTES   ON   PRACTICAL  MECHANICAL  DRAWING. 

several  planes  as  they  would  appear  if  made  of  trans- 
parent material. 

22.  The  V  and  H  planes  form  with  each  other  four 
dihedral  angles,  but,  for  purposes  of  representation  on  a 
drawing,  it  is  necessary  to  conceive  of  them  as  being 
folded  into  coincidence  with  each  other.  When  so  folding, 
they  revolve  about  the  G.L.  in  the  direction  of  the  arrows 
shown,  the  H  plane  being  revolved  into  coincidence  with 
the  Y  plane,  or  the  latter  revolved  into  coincidence  with 
the  H  plane  so  that  the  2nd  and  4th  angles,  as  designated 
in  Fig.  10,  close  up  to  0°,  while  the  1st  and  3rd,  unfold  to 
180° .  The  revolution  of  the  end  or  profile  plane  will  be 
discussed  a  little  later. 

*23.  A  is  a  point  in  space,  as  shown  in  Fig.  10  in  the 
first  dihedral  angle.  Its  projection  on  the  V  plane  is  the 
foot  of  the  perpendicular  to  the  V  plane  Aa ' .  Likewise 
its  projection  on  the  H  plane  is  the  foot  of  the  perpendic- 
ular to  the  H  plane  Aa. 

If  perpendiculars  are  dropped  from  a'  and  a  respect- 
ively to  the  G.L.,  they  will  intersect  the  G.L.  in  a  point, 
and  the  four  lines  together  make  a  rectangle. 

24.  The  distance  of  a '  from  the  G.L.  shows  the  distance 
of  the  point  from  the  H  plane  and  the  distance  of  a  from 
the  G.L.  shows  the  distance  of  the  point  from  the  V  plane. 
When  the  V  and  H  planes  are  folded  into  coincidence,  as 
in  Fig.  11,  the  perpendiculars,  let  fall  to  the  G.L.  from  a' 

*  The  notation,  which  will  be  used,  is  as  follows :  —  a',  b',  c',  etc.,  stand  for  the 
vertical  projections  of  points,  and  a,  6,  c,  etc.,  stand  for  the  horizontal  pro- 
jections of  the  same  points. 


ORTHOGRAPHIC  PROJECTION. 


23 


and  a,  become  one  and  the  same  line  perpendicular  to  the 
G.L.,  and  it  is  in  this  form  that  orthographic  projection 
deals  with  points,  lines,  etc. 


FlQUBK     NO.     11. 

b 


V  plane 
above  H. 


G. 


H  plane 
in  front  of  V. 


Also  H  plane  back 
of  V. 


L. 


Also  V  plane 
below  H. 


25.  The  projections  of  a  point  in  the  1st  angle,  2  inches 
from  V  and  3  inches  from  H,  in  V  projection,  would  be 
placed  3  inches  above  the  G-.L.,  and  in  H  projection  would 
be  put  on  a  perpendicular  to  the  G.L.  through  the  V  pro- 
jection, a  distance  of  2  inches  below  the  G-.L. 

If  it  were  required  to  show  the  projections  of  a  point 
which  was  in  the  3rd  angle,  1J  inches  from  V,  and  4  inches 
from  H,  the  V  projection  would  be  placed  4  inches  below 
the  G.L.,  and  on  the  same  perpendicular  to  the  G.L., 
through  it,  would  be  placed  the  H  projection  1J  inches 
above  the  G.L. 

If  a  point  is  in  one  of  the  co-ordinate  planes,  its  corre- 
sponding projection  is  in  the  G.L.,  that  is,  if  a  point  is  in 
the  V  plane,  its  H  projection  will  be  at  the  intersection 
with  the  G.L.  of  a  perpendicular  through  its  V  projection. 
If  a  point  is  in  both  co-ordinate  planes,  it  must  lie  at  their 


24 


NOTES   ON   PRACTICAL  MECHANICAL  DRAWING. 


intersection,  i.  e.,  be  in  the  G-.L.,  and  both  projections 
coincide  with  each  other,  and  with  the  point  itself. 

Further  discussion  of  the  principles  will  be  confined  to 
forms  in  the  3rd  angle  exclusively  as  this  is  more  common 
in  practice. 

26.  Lines  are  projected  by  projecting  points  on  the  line ; 
if  straight  lines,  the  projections  of  two  points  will  locate 
the  projections  of  the  line,  and  designate  the  position  of 
the  line  in  space  with  respect  to  the  co-ordinate  planes. 

FIG  TTRE    No.    12  . 


m 


Fig.  12  slioivs  the  several  projections  of  a  limited  line 
and  also  embodies  all  the  different  positions  which  a  line 
can  have  with  respect  to  the  co-ordinate  planes  in  the 
third  angle.  A  B  is  oblique  to  both  V  and  H,  since  the 
distances  of  A  from  both  V  and  H  are  different  from  those 
of  B.  CD  is  parallel  to  V  and  oblique  to  H  because  the 
distances  of  C  and  D  from  V  are  equal ;  JK  is  perpendic- 
ular to  V  since  the  line  connecting  j  and  k  is  perpendicular 
to  the  G-.L.,  and  coincides  with  the  projecting  line  of  both 
J  and  K  on  Y.  NO  lies  in  both  H  and  V,  i.  e.  in  the 
G.L.,  and  both  projections  of  N  and  0,  respectively, 
coincide  with  each  other.  This  group  of  projections  may 


ORTHOGRAPHIC  PROJECTION. 


25 


be  called,  appropriately,  the  alphabet  of  the  straight  line 
in  the  3rd  angle. 

If  a  line  is  parallel  to  a  coordinate  plane  its  projection 
on  that  plane  will  show,  (a),  the  true  length  of  the  line, 
and  (&),  by  its  angle  with  the  Gr.L.,  the  angle  the  line 
makes  with  the  other  or  corresponding  coordinate  plane. 

27.  The  projections  of  a  plane  figure  are  obtained  by 
projecting  separately  points  in  the  perimeter  of  the  figure 
and  connecting  the  projections  by  lines.  If  the  figure  is 
composed  of  a  curve  or  curves,  the  projections  of  a  con- 
venient number  of  points  of  the  curve  are  connected  by 
smooth  curves.  If  the  figure  is  composed  of  straight  lines, 
only  the  vertices  of  the  figure,  or  meeting  points  of  the 
edges,  need  be  projected. 


Fig.  13  illustrates  the  projections  of  a  plane  rectangular 
figure  in  different  positions  in  the  3rd  angle,  (a)  when  it  is 
perpendicular  to  H  and  oblique  to  V,  with  two  edges,  AB 
and  DC,  parallel  to  H,  (&)  when  it  is  perpendicular  to  V, 
and  inclined  to  H,  and,  (c)  when  it  is  oblique  to  both  H 
and  V,  with  two  edges  JK  and  ML,  parallel  to  both  H 
andV. 


26 


NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 


28.  A  solid  is  projected  upon  the  coordinate  planes  by 
projecting  points  on  the  surface  of  the  solid;  if  the  solid 
has  plane  faces,  these  points  are  usually  the  vertices 
where  three  or  more  faces  meet.  The  projections  will  be 
plane  figures  enclosing,  by  solid  lines,  the  largest  number 
of  points  and  those  edges,  which  are  hidden  by  the 
surfaces  of  the  solid,  are  shown  dotted. 

FIGURE  No.   14. 


ae 


i'e 


Figure  14  shows  a  cube  in  projection,  (a)  resting  on 
the  H  plane  with  four  faces  perpendicular  to  H  and  two 
parallel  to  V;  consequently,  each  edge  of  the  cube  is 
projected  upon  one  plane  its  true  length  and  upon  the 
corresponding  plane  as  a  point,  shown  by  the  designating 
letters  of  its  two  extremities;  (b)  a  cube  resting  with  one 
face  on  H  and  four  faces  oblique  to  V;  (c)  a  truncated 
hexagonal  pyramid.  The  notation  is  self  explanatory. 


ORTHOGRAPHIC  PROJECTION.  27 

29.  The  end  or  profile  projection  of  an  object  is  shown 
in  Fig.  15  in  the  third  angle.    The  upper  part  gives  a 
perspective  of  the  conditions,  the  lower,  the  orthographic 
projection  of   the    same.    Note  that   the    end    plane    is 
revolved  about  its    intersection  with  the    V   plane  and 
always  away  from  the  object.    The  arrow  in  the  figure 
helps  to  show  this  direction. 

30.  Any  plane  may  be  chosen  upon  which  to  project  an 
object;  it  need  not  be  either  vertical  or  horizontal,  but  may 
be  oblique  to  both  such  planes.    It  is  convenient  in  case 
it  is  desired  to  show  surfaces  their  full  size  and  shape  that 
are  oblique  to  V  and  H.    The  principles  of  projection  are 
the  same    and    the   auxiliary  plane,   as    it    is   called,   is 
revolved  about  its  line  of  intersection  with  V  or  H  into 
coincidence  with  one  or  the  other  of  the  latter. 

Fig.  16  shows  the  method  of  dealing  with  an  auxiliary 
plane.  The  upper  part  gives  a  perspective  of  the  condi- 
tions, the  lower,  the  orthographic  projection  of  the  same. 
The  auxiliary  plane  is  taken  parallel  to  the  oblique  or 
truncated  surface. 

31.  The  circle  is   projected   by  projecting  points,  and 
connecting  these  projections  by  a  line,  or  smooth  curve,  as 
the  case  may  be.    It  is  a  form  of  frequent  occurrunce  in 
constructive  work  and  deserves  to  be  thoroughly  compre- 
hended. 

It  is  convenient  to  circumscribe  the  circle  with  an 
auxiliary  square,  putting  this  into  projection  and  referring 
the  points  in  the  perimeter  of  the  circle  to  it. 


28  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 


Fl  GU  RE     NO  .     15. 


c 

b 

GE 

"*"- 

"*«s 

^\0 

X 

xs 

\         \ 
\         \ 
\        > 

\                 \ 

i 

\ 

•X 
N 

\    \ 

\ 

,G 

d 
d' 

a 

c'         H 

X 

\ 
\ 

\ 
\ 

\ 

V 

\ 

L 

V 

E. 

ce 

^\" 

^VY^ 

^>° 

/*& 

dc 

? 

( 

3e 

t 

>e 

ORTHOGRAPHIC  PROJECTION, 
FIGURE   No.  16. 


30  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 

FIGURES  Nos.   17,  18  AND   19. 


g 


Fig.  17  shows  the  projection  of  a  circle  whose  plane  is 
parallel  to  H.  In  this  position  its  projection  on  H  will  be 
a  circle  and,  upon  Y,  a  straight  line  equal  in  length  to  a 
diameter  of  the  circle,  as  GC.  The  points,  at  which  the 
circle  is  tangent  to  the  square,  and  those  in  which  it  cuts 
the  diagonals,  all  lie  in  V  projection,  upon  the  line  g'  cf , 
as  shown  in  the  figure. 

Fig.  18  shows  the  same  circle,  revolved  about  the  edge 
m  n  of  the  auxiliary  square,  until  its  plane  makes  an  angle 
of  60°  with  H.  Since  the  plane  is  perpendicular  to  V,  the 
angle  of  the  line  g'  c'  with  the  G-.L.  shows  the  angle  the 
plane  makes  with  H.  The  distances  of  the  various  points, 
in  the  perimeter  of  the  circle,  from  the  V  plane,  remain 
constant,  hence  the  distances  of  their  H  projections  from 


ORTHOGRAPHIC  PROJECTION.  31 

the  Gr.L.  is  constant,  and  they  may  be  transferred  from 
Fig.  17  by  parallels  to  the  Gr.L.  intersecting  perpendiculars 
to  the  Gr.L.,  through  the  V  projections  of  the  points, 
respectively,  as  shown. 

Fig.  19  shows  the  same  circle  when  its  plane  is  oblique 
to  both  H  and  V.  Its  projections  may  be  obtained  from 
those  of  Fig.  18,  by  conceiving  of  the  edge  m  n,  of  the 
auxiliary  square,  being  revolved  in  a  horizonal  plane 
through  any  desired  angle  about  the  point  m.  Since  the 
distances,  of  points  in  the  perimeter  of  the  circle,  from  the 
H  plane  are  constant,  the  new  H  projection  will  not 
change  its  shape;  and,  for  the  same  reason,  the  new  V 
projection  may  be  obtained  by  drawing  perpendiculars  to 
the  new  H  projections  of  the  points,  and  intersecting  par- 
allels to  the  G.L.,  through  the  V  projections  of  the  points, 
in  Fig.  18,  respectively. 

If  a  circle  is  parallel  to  a  coordinate  plane,  its  pro- 
jection on  that  plane  will  be  an  equal  circle,  and  its 
projection  on  the  corresponding  coordinate  plane,  to  which 
it  is  perpendicular,  is  a  straight  line.  In  any  other 
position,  the  projection  of  the  circle  is  an  ellipse,  the  proof 
of  which  properly  belongs  to  the  province  of  descriptive 
geometry. 

32.  Any  curve  in  general  may  be  projected  by  the  prin- 
ciples already  discussed,  namely,  by  projecting,  severally, 
points  in  the  curve,  or,  where  convenient,  circumscribing 
the  curve  by  a  simple  figure,  such  as  a  rectangle,  and 
referring  its  points  to  the  same. 

Working  drawings,  as  before  remarked,  are  made 
according  to  the  principles  of  orthographic  projection  that 


32  NOTES   ON  PRACTICAL  MECHANICAL,  DRAWING. 

have  been  discussed.  The  V  projection  corresponds  to  the 
'front  view,'  'front  elevation/  or  simply  'elevation/  as  the 
terms  are  variously  used,  and  the  H  projection,  to  the 
'plan.'  The  end  elevation  corresponds  to  the  'side  view,' 
'side  elevation,'  or  'end  view.'  The  auxiliary  projections 
discussed,  correspond  to  various  detail  views  of  parts  of  a 
subject,  which  may  have  their  edges  or  planes  oblique  to 
the  principal  coordinate  planes  upon  which  the  subject 
may  be  projected. 

33.  The  difference  between  1st  angle  and  3rd  angle  pro- 
jection. For  wrorking  drawings,  the  choice  is  open  of 
either  the  first  angle,  or  the  third  angle.  In  either  the 
second  or  the  fourth,  the  plan  is  quite  likely  to  fall  behind 
or  in  front  of  the  elevation.  If  the  distances  of  the  eleva- 
tion and  plan,  from  the  ground  line,  are  made  to  differ  by 
a  sufficient  amount,  this  super-position  can  be  avoided,  but 
an  equal  difficulty  is  encountered,  in  not  being  able  to 
distinguish  which  is  second  angle,  and  which  is  fourth 
angle,  for  the  relation  of  plan  to  elevation  does  not 
determine  it. 

In  the  first  angle  projection,  the  object  is  projected 
upon  the  vertical  plane,  from  a  center  of  projection,  wnich 
is  assumed  to  be  on  the  same  side  of  the  plane  as  the 
object;  this  is  also  true  of  the  horizontal  projection.  To 
be  consistent,  an  end  view  of  the  object  should  be  that 
obtained,  by  projecting  it  from  a  center  on  the  same  side 
of  the  plane  as  the  object.  For  illustration :  The  view  of 
the  left  hand  end  of  an  object  would  be  placed  on  that 
plane,  which  was  to  the  right  of  the  object,  and  the  view 
of  the  right  hand  end  would  be  projected  upon  the  plane  at 


ORTHOGRAPHIC  PROJECTION.  33 

the  left.  Now,  if  the  same  center  is  used,  and  an  object  is 
drawn  in  vertical  projection,  in  the  third  angle,  it  will  be 
projected  through  the  vertical  plane,  for  the  center  is  on 
the  opposite  side  of  the  plane  from  the  object.  Therefore, 
to  be  consistent,  the  end  view  should  be  obtained  by  use 
of  a  center,  which  is  upon  the  opposite  side  of  the  plane 
from  the  object.  If  this  is  done,  the  view  of  the  left  hand 
end  of  an  object  will  lie  at  the  left,  and  that  of  the  right 
hand  end  at  the  right. 

It  is  convenient  to  have  this  latter  condition  of  affairs 
in  a  working  drawing,  because  it  conduces  to  legibility, 
and,  in  fact,  it  has  been  quite  universally  adopted.  Care 
should  be  taken  by  the  beginner  not  to  be  thoughtless  in 
the  use  of  either  angle  at  pleasure,  and  in  not  mixing  the 
two  in  a  drawing. 

Figures  20  and  21  show  the  1st  and  3rd  angle  projec- 
tions of  an  object  respectively. 

34.    *  Problems  in  projection. 

(1.)  Draw  the  projections  of  the  following  points. 
(a.)  li  inches  from  H,.l  inch  from  V.  (&.)  f  inch  from 
V  and  li  inches  from  H.  (c.)  In  Y  1J  inches  from  H. 
(d.)  In  H  4 'inch  from  V.  (6.)  In  the  G.L. 

(2.)  Draw  the  projections  of  the  following  lines, 
making  either  projection  on  V  or  H  not  over  !£  inches 
long,  (a.)  Oblique  to  V  and  H,  nearest  end  to  Y,  J  inch 
from  it.  (b.)  Parallel  to  H  and  oblique  to  V.  (c.) 
Parallel  to  V  and  oblique  to  H.  (d.)  Perpendicular  to 
H,  J  inch  from  Y.  (e.}  Perpendicular  to  Y,  and  1  inch 
from  H.  (/".)  Parallel  to  both  Y  and  H,  1  inch  from  Y 

*To  be  drawn  in  3rd  angle  projection  unless  otherwise  directed. 


34  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 

FIGURE  No.  20. 
ILLUSTRATING  FIRST   ANGLE   PROJECTION. 


ORTHOGRAPHIC  PROJECTION. 
FIQUBK    NO.    21. 

ILLUSTRATING   THIRD    ANGLE    PROJECTION. 


35 


36  NOTES   ON   PRACTICAL  MECHANICAL  DRAWING. 

and  J  inch  from  H.  (g.)  Parallel  to  and  equi-distant 
from  V  and  H. 

(3.)  Draw  the  projections  of  a  rectangle  of  edges  1 
inch  x  1J  inches,  (a.)  Place  it  so  that  it  is  parallel  to  V 
and  distant  $  inch  from  H.  (&.)  Place  it  so  that  it  is 
perpendicular  to  V  and  inclined  at  an  angle  of  45°  to  H. 
(c.)  Place  it  so  that  an  edge  rests  on  H,  its  plane  making 
an  angle  of  45°  with  H  and  the  edge  upon  which  it  is  rest- 
ing, at  an  angle  of  60°  with  V.  NOTE  :  —Place  it  first  per- 
pendicular to  V,  at  the  required  angle  with  H,  and  then 
revolve  it  into  the  final  position,  which  will  be  oblique  to 
both  H  and  V. 

(4.)  Draw  an  equilateral  triangle  in  projection  of  If 
inches  on  edge.  So  placed  that  an  edge  lies  in  Y  at  an 
angle  of  30°  to  H,  and  the  plane  of  the  triangle  is  at  60° 
toV. 

(5.)  Draw  a  circle  in  V  and  H  and  end  projection; 
the  circle  to  be  2  inches  in  diameter,  perpendicular  to  H, 
and  making  an  angle  of  60°  with  V. 

(6.)  Draw  the  square  pyramid,  in  projection,  of 
dimensions  as  shown,  the  base  parallel  to  and  3  inches 
from  H,  the  edges  of  base  at  30°  and  60°  respectively  to  V. 

(7.)  Draw  the  pyramid  of  problem  6  in  projection 
showing  also  an  end  view,  so  placed  that  the  plane  of  the 
base  is  perpendicular  to  V  and  makes  an  angle  of  30°  with 
the  H  plane. 

(8.)  Draw  the  hexagonal  prism  of  dimensions  shown 
in  V,  H,  and  end  projection,  with  a  hexagonal  base,  rest- 
ing on  the  H  plane,  two  rectangular  faces  parallel  to  V. 

(9.)  Draw  the  hexagonal  prism  of  problem  8,  so 
placed  that  an  edge  of  hexagonal  base  rests  on  H  at  30°  to 


ORTHOGRAPHIC  PROJECTION. 


37 


0. 


V,  with  plane  of  base  at  45°  to  H.  Show  V  and  H  pro- 
projections.  Project  the  same  upon  an  auxiliary  V  plane 
which  is  perpendicular  to  the  hexagonal  bases. 

(10.)  Draw  the  square  prism  shown,  with  square  base 
resting  on  H,  and  rectangular  faces  at  angles  of  30°  and 
60°  with  V  respectively. 

(11.)  Draw  the  square  prism  of  problem  10,  placing 
it  so  that  it  rests  on  a  short  edge,  on  H,  the  edge  mak- 
ing an  angle  of  60°  with  V,  and  the  plane  of  the 
square  base  at  an  angle  of  60°  to  H.  NOTE:— Draw  the 
prism  first  with  two  rectangular  faces  parallel  to  V,  and 
then  obtain  the  final  position  by  projecting  upon  ar 
auxiliary  or  Vi  plane  at  an  angle  of  60°  with  V. 

(12.)  Draw  the  truncated  hexagonal  prism  shown,  so 
placed  that  a  hexagonal  base  is  in  H  and  all  vertical  faces 
oblique  to  V.  The  plane  of  the  top  is  at  an  angle  of  30° 


38 


NOTES   ON   PRACTICAL  MECHANICAL  DRAWING. 


10. 


12. 


to  H.    Show  the  true  shape  of  the  section  by  projection 
on  an  auxiliary  plane.    Assume  dimensions  not  shown. 

(13.)  Draw  the  top,  front  and  side  views  of  block 
shown.  Take  the  dimensions  from  the  figure  with  the 
dividers,  as  they  are  represented  in  the  picture  their  true 
size. 


13. 


CHAPTER   III. 
ISOMETRIC  AND  OBLIQUE  DRAWING. 

35.  Isometric  drawing,  meaning  a  drawing  of  equal 
measurement,  is  one  which  shows  form  and  correct 
dimensions,  within  certain  limits,  in  one  view.  Ortho- 
graphic projection  ordinarily  requires  two  views  of  an 
object  upon  planes  at  right  angles  to  each  other,  after- 
wards revolved  into  coincidence.  A  perspective  drawing 
on  the  other  hand,  represents,  by  one  view,  the  object  as 
it  would  appear  from  some  particular  point,  giving  a 
pictorial  representation,  but  not  th^  exactness  of  shape,  or 
the  possibility  of  measurement  required  in  a  mechanical 
drawing,  Isometric  drawing  combines  both  of  these,  and 
shows  the  three  dimensions,  length,  breadth  and  thickness 
in  one  view  and  at  the  same  time  admitting  of  measure- 
ment. It  gives  a  somewhat  distorted  appearance  to 
objects,  for  that  reason  its  application  is  limited  to  objects 
of  simple  shape. 

An  isometric  drawing 
may  be  derived  as  follows: 
If  a  cube  is  projected  upon  a 
plane,  to  which  all  of  its  faces 
are  equally  inclined,  the  re- 
sult will  look  like  Fig.  22,  and 
is  an  isometric  projection  of 
the  cube.  All  edges,  as  well 
as  plane  faces,  are  equally 
foreshortened ;  and,  since 


FIGURE  No .  22. 


40 


NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 


this  is  true,  all  edges  may  be  extended  until  they  are  equal 
in  length  to  the  edges  of  the  cube,  without  affecting  the 
proportional  relations  when  we  have  an  isometric  drawing. 

The  principles  of  isometric  drawing  are  derived  from 
this  treatment  and  are  as  follows : 

(a.)  There  are  three  lines  called  isometric  axes, 
making  angles  of  120°  with  each  other.  These  lines  may 
have  any  position  depending  upon  the  position  of  the 
object,  but  usually  those  illustrated  in  Fig.  23. 

FIGURE    No.    23. 


(b.)  These  lines  or  isometric  axes,  represent  lines 
which  are  at  right  angles  to  each  other. 

(c.)  Upon  these  lines,  or  lines  parallel  to  them,  the 
dimensions  of  length,  breath  and  thickness  are  measured. 
All  such  lines  are  called  isometric  lines.  Any  other  lines 
are  'non-isometric,  and  their  position  and  length  must  be 
obtained  by  reference  to  some  isometric  lines. 

(d.)  Parallel  lines  on  an  object  are  always  parallel 
on  the  drawing. 

Fig.  24  also  shows  by  the  dotted  lines  how  a  cube 
would  look  in  isometric  drawing. 

Objects,  composed  of  non-isometric  lines,  must  first 
be  surrounded  by,  or  referred  to,  an  object  of  some 


ISOMETRIC  AND   OBLIQUE  DRAWING. 


41 


FIGURE  No.  24. 


isometric  construction,  and  the  lines  of  the  object  are 
then  referred  to  these  isometric  lines.  For  example, 
consider  the  treatment  of  a  pyramid,  see  Fig.  25. 


FlGUBE    NO.    25. 


42  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 

Curves  in  isometric  drawings  are  obtained  by  locating 
a  sufficient  number  of  points  with  reference  to  some 
isometric  lines,  as  in  Figure  26. 

FIGURE  No.  26.  FIGURE  No.   27. 


An  approximate  method  for  an  isometric  drawing  of  a 
circle  is  shown  in  Fig.  27. 

36.  Oblique  projection  is  somewhat  like  isometric 
projection.  In  most  cases  its  apparent  distortion  is 
greater  than  in  isometric  drawing,  yet  it  possesses  several 
distinct  advantages;  the  principal  one  being  that  two 
dimensions  are  represented  in  their  true  direction  as  well 

FlQTJKK    NO.    28. 


ISOMETRIC  AND   OBLIQUE  DRAWING.  43 

as  size,  giving  one  face  in  its  true  form  as  shown  in  Fig. 
28.  The  principles  of  oblique  projection  are  as  follows: 
(a.)  One  face  of  the  object  is  taken  parallel  to  the  plane 
of  projection.  On  this  face  two  dimensions  are  measured. 
(6.)  All  lines  perpendicular  to  this  face  are  made  45° 
lines  on  the  drawing.  On  these  lines  the  third  dimension 
is  measured  its  true  length.  (This  is  not  strictly  true 
oblique  projection,  but  differs  from  it  in  a  similar  way  that 
isometric  drawing  differs  from  isometric  projection.) 


CHAPTER   IV. 
USE    OF    INSTRUMENTS. 

37.  Practical  points  about  drawing  materials  and  in- 
struments. A  student's  first  lesson  to  learn,  and  a 
teacher's  first  duty,  is  to  teach  the  proper  use  and  care  of 
tools.  With  this  lesson  learned,  it  should  be  possible  for 
the  beginner  to  work  safely  with  the  best  appliances,  and 
the  best  are  none  too  good.  It  is  the  purpose  now  to  say 
something  about  the  different  tools  and  their  proper  care 
and  handling. 

Drawing  boards:  The  best  drawing  boards  are  made  of  well 
seasoned  pine,  of  uniform  grain,  narrow  strips  glued  together,  the 
whole  being  finished  at  the  two  opposite  ends  at  right  angles  to  the 
strips  by  narrow  pieces  tongued  and  grooved  and  glued  to  the 
board,  to  prevent  warping.  In  large  boards  of  first-class  construc- 
tion, battens  are  fastened  to  the  back  of  the  board,  so  as  to  permit 
of  expansion  and  contraction  of  the  board  with  changing  tempera- 
ture, but  not  of  warping.  This  is  effected  by  fastening  a  batten 
rigidly  at  one  point  near  the  middle,  and  at  two  or  more  other 
points  by  screws,  rigid  in  the  board,  but  working  in  slots  in  the 
batten.  In  order  to  still  further  lessen  the  tendency  of  the  board 
to  warp,  saw  cuts  or  grooves  are  made  about  two  inches  apart, 
longitudinal  of  the  strips  of  which  the  board  is  constructed,  and 
of  a  depth  of  about  half  the  thickness  of  the  board. 

It  is  not  absolutely  necessary  that  all  four  edges  of  a  board 
should  constitute  a  true  rectangle,  they  ought  to  be  straight.  Only 
one  edge  of  a  board,  the  left  hand  edge,  should  be  used  upon  which 
to  rest  the  T  sq.  head,  the  triangles  should  be  used  for  vertical 
lines. 

The  under  side  of  a  battened  drawing  board  may  conveniently 
be  used  to  cut  paper  on,  but  it  should  never  be  done  on  the  working 


USE   OF   INSTRUMENTS. 


45 


side,  and  care  should  be  exercised  that  the  working  side  and  the 
edges  of  the  board  be  kept  clean  and  in  all  respects  in  good  order. 

Tee  squares  are  made  in  various  forms.  They  should  be  of 
well  seasoned  wood  of  uniform  grain.  The  blade  may  be  sunk  in 
the  head  or  screwed  on  top  and  glued.  A  frequent  source  of 
trouble  in  T  sqs.  is  that  the  part  of  the  head  just  under  the  blade 
swells  under  the  action  of  the  moisture  in  the  glue  when  it  is 
made,  becomes  set,  and  causes  the  head  to  rock  against  the  edge  of 
the  board  when  in  use.  The  bulge  in  the  head  can  be  seen  by 
placing  a  straight  edge  against  it.  An  excellent  form  of  T  sq.  is 
made  of  mahogany,  with  a  very  narrow  edging  of  ebony.  The 
latter  is  particularly  hard,  it  relieves  the  edge  by  its  strong 
contrast  with  the  color  of  the  paper.  Sometimes  a  celluloid  edge 
is  used.  This  seems  to  have  growing  favor  because  of  its  trans- 
parency, permitting  partial  sight  of  the  work  underneath.  If  T 
sqs.  are  large,  they  are  tapered  as  before  mentioned,  so  that  the 
upper  edge  is  the  only  one  that  can  be  used. 

Some  T  sqs.  are  made  with  a  swivel  head  so  that  the  angle  of 
the  blade  can  be  adjusted,  and  they  have  their  value.  It  may  be 
said  that  one  should  be  in  a  large  and  well  equipped  drafting  office, 
but  that  for  ordinary  use  it  is  not  necessary.  Steel  T  sqs.  are 
made,  but  are  not  favorities  with  draftsmen  because  of  their 
weight  and  the  danger  of  injury  to  the  drawing  by  denting,  etc. 

Triangles  are  made  of  the  same  materials  as  the  T  sqs.,  solid 
triangles,  however,  are  not  good  as  they  will  warp.  Triangles  are 
made  also  of  vulcanized  rubber  and  of  celluloid.  The  former  have 
the  advantage  of  contrasting  well  with  the  color  of  the  paper,  but 
they  have  the  disadvantage  of  being  non-absorbent,  consequently 
they  transfer  dirt  from  one  part  of  the  drawing  to  another  and  are 
apt  to  smear  it.  The  inside  edges  of  a  triangle  may  have  depres- 
sions cut  in  them  to  facilitate  picking  up  from  the  paper. 

A  30°  and  a  60°  triangle  and  a  45°  triangle  are  the  only  two  in 
common  use  except  those  especially  made  for  mechanical  lettering. 
Some  other  angles  may  be 'struck  by  using  the  triangles  together 
and  adding  or  subtracting  their  angles  to  get  15°,  75°,  etc. 

Paper  comes  of  various  kinds  and  quality,  suited  to  different 
kinds  of  drawing.  A  moderately  heavy  grade  with  smooth,  hard 


46  NOTES   ON   PRACTICAL  MECHANICAL  DRAWING. 

surface  is  to  be  desired  for  mechanical  drawings.  A  yellow  or 
manilla  paper  is  much  used  for  pencil  drawings,  when  the  result- 
ing drawing  is  to  be  traced;  it  is  called  detail  paper.  Bond  paper 
has  also  come  quite  into  use,  and  it  has  distinct  advantages. 
The  drawing  is  penciled  and  inked  on  the  paper  and  from  it  blue 
prints  can  be  readily  made.  Paper  should,  if  possible,  never  be 
rolled,  particularly  rolled  small  as  it  cannot  be  satisfactorily 
flattened  again. 

Tracing  cloth  is  in  almost  universal  use  in  drafting  rooms  for 
permanent  drawings,  as  blue  prints  can  be  so  readily  made  from 
it.  Either  the  rough  or  the  smooth  side  can  be  equally  well  used 
for  drawing  in  ink.  Frequently  the  original  pencil  drawing  is 
made  upon  the  rough  side  of  the  cloth  and  inked  over.  It  fur- 
nishes a  very  good  surface  for  this  purpose.  The  smooth  side  is 
impractical  for  pencil  drawings  but  takes  ink  like  a  highly  cal- 
endered surface.  Special  precautions,  which  will  be  mentioned 
shortly,  have  to  be  observed  in  working  upon  it.  There  is  but  one 
recognized  grade  and  make  of  tracing  cloth,  the  "Imperial." 

Stretching  of  paper,  as  it  is  called,  is  resorted  to  where  any 
water  color  brush  work  is  to  be  done.  It  consists  of  pasting  the 
edges  to  the  board  and  shrinking  until  it  is  quite  taut.  It  takes  a 
little  experimenting  to  get  facility  in  doing  this,  but  every  one 
ought  to  know  how  to  do  it  when  occasion  arises,  hence  the 
following  directions  are  appended. 

*  "To  stretch  paper  tightly  on  the  board,  lay  the  sheet  right 
side  up — which  side  is  presumably  the  one  which  shows  correct 
reading  of  the  water  mark  when  held  to  the  light— place  a  rule  with 
its  edge  about  one-half  inch  back  from  each  edge  of  the  paper  in 
turn,  and  fold  up  against  it  a  margin  of  that  width.  Then  thor- 
oughly dampen  the  back  of  the  paper  with  a  full  sponge,  except  on 
the  folded  margins.  Turning  the  paper  again  face  up,  gum  the 
margins  with  strong  mucilage  or  glue,  and  quickly  but  firmly 
press  opposite  edges  down  simultaneously,  long  sides  first,  exert- 
ing at  the  same  time  a  slight  outward  pressure  with  the  hands  to 
bring  the  paper  down  somewhat  closer  to  the  board.  Until  the  gum 
sets  so  that  the  paper  adheres  perfectly  where  it  should,  the  latter 

*  F.  N.  Willson's  Theoretical  and  Practical  Graphics,  p.  14. 


USE  OF  INSTRUMENTS.  47 

should  not  shrink;  hence,  the  necessity  for  so  completely  soaking 
it  at  first.  The  sponge  may  be  applied  to  the  face  of  the  paper 
provided  it  is  not  rubbed  over  the  surface  so  as  to  damage  it.  The 
stretch  should  be  horizontal  when  drying,  and  no  excess  of  water 
should  be  left  standing  on  the  surface;  otherwise  a  watermark 
will  form  at  the  edge  of  each  pool." 

The  compass,  dividers,  bow  instruments  and  ruling  pen  consti- 
tute the  simple,  universal  kit,  and  probably  the  majority  of 
draftsmen  have  little  else.  Of  course  there  are  a  number  of  other 
tools  made,  chiefly  for  special  uses.  These  are  not  used  univer- 
sally, however,  because  the  time  saved  with  a  special  tool  is 
usually  offset  by  the  time  consumed  in  handling  and  cleaning,  for 
each  special  tool  comes  in  generally  for  but  occasional  and  brief 
use.  Somewhat  similar  reasons  explain  why  various  special 
attachments  to  the  simple  kit  are  not  popular  universally,  like 
hair  spring  legs  in  compass  and  dividers,  spring  catch  ruling  pens, 
micrometer  adjustment  to  needle  point,  etc. 

Beam  compasses  are  instruments  to  strike  large  circles,  consist- 
ing of  a  needle  point  leg  and  marking  point  leg,  each  separate  and 
adjustably  mounted  upon  a  bar  of  metal  or  wood.  Every  large 
drafting  room  is  likely  to  have  one  for  occasional  use,  but  the 
individual  hardly  needs  to  go  to  the  expense  of  one  unless  its  use 
is  demanded  frequently. 

Follower  pens,  in  which  the  pen  is  swiveled  in  the  handle,  are 
used  to  make  irregular  curves.  The  pen  automatically  adjust* 
itself  properly  to  the  ruling  edge.  It  has  but  occasional  use. 

A  bow  pen,  made  chiefly  for  special  professions,  has  a  fixed 
needle  point  leg  with  a  marking  leg  sliding  freely  upon  it.  It  is 
handy  for  striking  a  large  number  of  circles  of  small  diameter, 
but  it  is  a  tool  for  that  special  purpose. 

Dotting  Wheels  are  instruments  to  do  what  the  name  implies, 
make  dotted  lines.  They  .also  have  occasional  use  but  are  a 
trouble  to  care  for  and  easily  get  out  of  order. 

Proportional  dividers,  consisting  of  double  pointed  legs,  pivoted 
between  the  ends,  and  adjustable,  so  as  to  give  a  range  of  relation 


48  NOTES   ON  PRACTICAL  MECHANICAL,  DRAWING. 

between  the  opposite  angles  formed,  are  a  very  useful  tool  indeed 
upon  those  rare  occasions  when  a  drawing  is  merely  to  be  copied 
to  a  different  size  regardless  of  scale.  Where  scale  is  desired  it 
is  not  safe  as  a  tool  nor  is  it  much  handier  than  the  scale  direct. 

A  parallel  straight  edge  is  made  which  replaces  the  T  sq.  A 
rule,  of  the  length  of  the  board,  is  held  at  the  ends  by  sliding  on  a 
wire  cable  and  moves  into  parallel  positions.  Theoretically  it  is 
excellent  but  lack  of  sufficient  rigidity  is  its  chief  drawback  in  the 
opinion  of  many. 

The  protractor  is  a  semi-circular  disc  segment  of  celluloid, 
bone  or  brass  with  degrees  marked  upon  it.  The  center  is  marked 
on  the  straight  edge  of  it.  It  has  use  where  angles  have  to  be 
struck  of  varying  sizes  and  other  than  those  for  which  the  tri- 
angles can  be  used. 

There  is  a  machine  on  the  market  known  as  the  Universal 
Drafting  Machine,  which  has  very  meritorious  features.  It  com- 
bines the  function  of  the  T  sq.,  triangles  and  scales,  and,  when 
specially  adjusted,  the  protractor. 

It  consists  essentially  of  two  straight  edges  with  scales  upon 
them  and  with  a  common  point  of  attachment.  They  can  be  set 
rigidly  at  any  angle  to  one  another  and  the  whole  moved  in  any 
direction  over  the  board  through  the  medium  of  hinged  arms, 
rigidly  attached  to  the  upper  left  hand  corner  of  the  drawing  board. 
Straight  edges,  having  any  of  the  standard  scales  upon  them,  may 
be  attached  to  the  frame. 

There  is  also  a  Paragon  Drafting  Instrument  accomplishing 
much  the  same  purpose.  It  is  attachable  to  a  parallel  ruler 
previously  mentioned  or  it  can  be  attached  to  a  T  sq.  blade.  The 
fixed  center  is  the  point  of  attachment  and  the  ruling  edges,  two 
in-  number,  can  be  swung  around  it  at  any  angle,  replacing  tri- 
angles and  protractor,  and  also  having  variously  scaled  edges. 

38.     Some  practical  points  about  and  the  care  and  hand- 
ling of  drawing  instruments. 

Drawings  can  be  cleaned  of  dirt  with  the  soft  pliable 


USE  OF  INSTRUMENTS.  49 

erasers,  the  kneaded  rubber,  the  sponge  rubber  or  stale 
bread  crumbs  rubbed  over  with  a  cloth  or  with  the  hand. 
The  liquid  drawing  inks  will  stand  very  little  erasure  with 
the  pencil  eraser  without  loss  of  blackness  in  the  lines.  To 
keep  a  drawing  in  good  shape  as  the  work  progresses, 
cultivate  early  the  habit  of  keeping  the  T  sq.  and  triangles 
clean,  using  a  piece  of  paper  where  possible  over  parts  of 
the  drawing  not  in  immediate  use,  and,  finally,  keeping 
the  hands  off  the  work  when  they  are  not  in  active  service. 

Be  careful  to  use  the  tools  only  for  the  purposes  for  which 
they  were  intended.  Violations  of  this  are  to  be  found  in 
using  the  T  sq.  as  a  hammer  to  put  in  tacks,  the  dividers 
as  compasses  to  describe  arcs,  sticking  the  divider  points 
into  the  board  so  the  dividers  will  stand  alone,  etc.,  all  of 
which  tend  to  injure  the  tools. 

The  tools  should  be  at  all  times  handy.  With  the  T  sq. 
always  on  the  board,  the  triangles  above  it  on  the  board 
and  other  tools  in  predetermined  places  from  which  they 
can  be  picked  up  without  much,  if  any,  hunting,  and  while 
the  eyes  are  engaged  on  the  drawing,  will  conduce  to 
rapidity  and  accuracy  of  work.  Observe  that  the  work- 
man in  any  craft  will  always  lay  a  tool  down  when  he  is 
done  with  it,  even  temporarily,  and  moreover,  he  lays  it 
down  where  it  is  the  least  trouble  to  find  it  again. 

Facility  in  the  use  of  the  ruling  pen  is  eminently  desira- 
ble, hence  a  few  more  practical  directions  are  here  given: — 

The  greater  care  at  all  times  should  be  exercised,  the 
thicker  the  line  used  or  the  fuller  the  pen  is  with  ink.  The 
beginner  should  carry  less  ink  in  the  pen  than  after  he 
becomes  an  expert.  When  occasion  arises  to  use  the  pen 
for  long  lines  or  many  close  together,  with  the  least  inter- 


50  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 

ruption  for  refilling,  a  considerable  amount  of  ink  can  be 
carried  in  the  pen  if  the  following  directions  are  observed: 
Head  the  pen  to  start,  the  point  very  close  to  but  not  touch- 
ing the  paper;  when  ready,  touch  the  pen  to  the  starting 
point  and  instantly  move  on  the  line  uniformly  and  rapidly, 
the  more  rapidly  the  fuller  the  pen.  Stop  and  lift  the  pen 
in  the  same  instantaneous  way.  These  same  precautions 
hold  when  making  a  very  thick  line  with  the  pen;  the 
thicker  the  line  the  less  ink  can  be  carried. 

In  drawing  lines  to  go  from  or  to  a  heavy  ink  line  or 
border  still  greater  care  has  to  be  observed  that  the  border 
does  not  draw  the  ink  out  of  the  pen  and  cause  a  blot.  The 


FIGURE  No. 


situation  is  illustrated  in  Fig.  29.  It  shows  a  series  of  lines 
close  together  where  the  edges  of  the  lines  are  apt  to  break 
down  and  the  lines  run  together.  In  cases  of  great  danger, 
every  other  line  or  so  may  be  begun  late  as  shown  in  the 
figure  and  afterwards  filled  out  when  the  ink  dries.  In 
patching  these  open  spaces  set  the  pen  to  make  a  finer 
line,  matching  only  one  edge  of  the  line  drawn,  then  by 
tilting  the  pen  probably  the  requisite  increase  can  be  made 
if  not  with  accuracy  in  one  stroke,  then  in  two  or  more;  a 
line  can  be  added  to  easily  but  it  cannot  be  reduced  in  size, 
except  by  erasure  first  and  then  redrawing. 

//  a  pen  fails  to  work  it  may  be  due  to  several  causes. 

(a.)  It  may  be  set  so  tight  that  the  ink  cannot  flow 
out  between  the  nibs. 


USE  OF  INSTRUMENTS.  51 

(&.)  The  ink  may  have  dried  at  the  ends  of  the  nibs, 
if  not  farther,  and  clogged  the  flow.  The  best  thing  to-  do 
is  to  at  once  clean  and  refill.  The  use  of  the  blotter  or  a 
piece  of  paper  drawn  through  between  the  nibs  is  to  be 
deprecated. 

(c.)  If  the  ink  does  not  run  down  to  the  point,  proper 
running  may  be  facilitated  by  opening  the  nibs  a  little  and 
shaking  gently,  over  a  blotter  or  something  it  will  not 
injure  if  it  blots,  until  the  ink  settles  or  drops  out.  The 
difficulty  is  caused  by  grease  on  the  inside  of  the  nibs. 

(d.)  The  pen  point  may  be  actually  out  of  order. 
This  of  course  demands  that  it  be  sharpened ;  but  the  pen 
should  be  tested  for  all  the  other  difficulties  first.  An 
injured  pen  will  either  not  mark  at  all  or  it  will  make  a 
ragged  line ;  the  line,  moreover,  may  be  ragged  at  one  or 
both  edges.  If  the  pen  is  merely  uniformly  dull,  it  will 
refuse  to  make  a  fine  line,  the  line  will  simply  fail  entirely 
if  the  nibs  are  brought  close  together. 

A  pen  can  be  sharpened  and  tested  in  the  following  manner: 
A  fine  oil  stone  should  be  used  for  this,  an  Arkansas  stone  seems 
to  be  preferred.  Bring  the  nibs  of  the  pen  together  as  for  drawing 
a  very  fine  line,  and  hold  for  the  rubbing  at  a  small  angle  to  the 
stone,  30°  or  less,  and  with  the  broad  face  of  the  nibs  towards  the 
stone.  Rub  to  and  fro  in  the  direction  of  the  handle  with  at  the 
same  time  a  slight  rocking  of  the  pen  in  order  to  round  the  point. 
If  too  pointed  it  tends  to  cut  into  the  paper  and  will  not  hold 
sharpness  so  long.  To  test  for  sharpness,  drag  it  on  a  piece  of 
paper  as  if  making  a  line;  it  ought  not  to  scratch  roughly  or  glide 
too  freely,  but  bite  slightly,  that  is,  resist  motion.  If  it  seems  to 
act  as  it  should,  clean  thoroughly  and  then  try  with  ink.  Properly 
sharpened,  the  pen  should  make  a  very  fine  black  hair-line  without 
breaking  and  a  broad  line  of  sharp  edges,  even  if  the  pen  is  tilted 
five  or  six  degrees  out  of  plumb  in  a  plane  perpendicular  to  the 
ruling  edge.  Try  for  a  broad  line  first  with  this  test  in  order  to 


52  NOTES    ON   PRACTICAL  MECHANICAL  DRAWING. 

see  if  both  sides  are  of  equal  length.  If  they  are  not,  that  side  of 
the  line  at  which  the  nibs  are  shortest  will  show  ragged.  If  this 
test  is  successful  and  the  line  drawn  is  perfectly  sharp  and  clear 
on  its  edges,  test  for  fineness  of  line,  by  working  from  a  wide  line 
towards  a  narrow  one.  If  it  happens  that  the  sharpening  has  pro- 
ceeded too  far  and  the  pen  bites  too  deeply  into  the  paper,  or  if  one 
nib  is  slightly  longer  than  the  other,  the  pen  may  be  dulled  or  the 
long  nib  worn  down  by  rubbing  it  on  the  stone  with  a  rotary 
motion  when  the  broad  nibs  of  the  pen  lie  in  a  plane  perpendicular 
to  the  plane  of  the  stone. 

To  determine  the  place  of  a  line  the  ruling  edge  should 
furnish  a  rough  approximation  and  the  marking  point  the 
exact  place.  It  is  one  of  the  important  points  in  handling 
to  be  learned  early.  The  nibs  of  a  ruling  pen,  for  example, 
being  bowed,  will  touch  the  paper  slightly  beyond  the  ruling 
edge.  If  the  pen  is  incorrectly  tilted  until  the  nibs  touch 
the  paper  at  the  ruling  edge,  a  blot  is  almost  sure  to  result, 
for  the  ink  will  touch  the  ruling  edge. 

It  may  sometimes  happen,  when  a  number  of  lines 
have  to  be  drawn  which  run  in  a  variety  of  directions,  that 
waste  of  time  is  threatened  in  waiting  for  ink  to  dry.  The 
ruling  edge  can  be  held  slightly  free  of  the  paper  and'  over 
the  wet  lines  by  using  the  thumb  and  first  or  second  finger 
as  a  cushion  underneath  it  or  one  ruling  edg;e  may  be 
rested  on  and  slightly  overhanging  another.  In  small  work 
one  triangle  may  be  put  with  its  open  space  over  the  lines 
to  be  drawn,  and  the  other  triangle  rested  upon  it,  crossing 
the  gap.  A  method  of  inking  will  be  shortly  discussed 
which  overcomes  some  difficulties  of  waiting  for  ink  to  dry. 

Errors  in  an  ink  drawing  can  be  corrected  so  that  the 
repairs  are  practically  invisible.  A  knife  will  not  do  this 
unless  used  in  conjunction  with  the  ink  eraser.  In  fact, 
cutting  or  scratching  with  a  knife  is  so  risky  that  it  is  safe 


USE   OF  INSTRUMENTS.  53 

to  adopt  the  custom  of  never  using  it  except  under  extreme 
circumstances. 

If  an  error  occurs,  take  up  as  much  ink  as  possible  with 
a  blotter,  but  do  not  use  it  under  any  ordinary  circum- 
stances to  dry  a  line  because  it  pales  the  ink.  Then  use 
the  ink  eraser,  rubbing  rather  lightly  and  rapidly,  not  in 
one  direction  or  with  one  part  of  the  eraser,  but  in  all 
directions  and  changing  the  point  of  contact,  because  the 
rubber  will  heat  and  not  work  so  well.  Every  vestige  of 
the  mistake  should  thus  be  removed,  although  it  blurs  a 
certain  area  around  the  error.  Next  clean  off  all  the  sand 
by  using  the  pencil  eraser.  If  the  surface  of  the  paper  is 
very  much  disturbed  it  may  be  necessary  to  burnish  it  with 
a  piece  of  ivory  or  smooth  metal.  The  difficult  part  of 
correcting  errors  comes  in  putting  back  the  ink  lines.  A 
line  made  upon  an  erased  space  is  quite  apt  to  spread  and 
show  larger  than  on  the  fresh  paper,  although  the  differ- 
ence is  very  slight,  therefore  the  pen  should  be  set  for  a 
slightly  finer  line,  and  this  added  to  by  successive  strokes. 
If,  in  spite  of  all  precautions,  the  place  erased  be  treacher- 
ous, use  two  exceedingly  fine  lines  as  limits  or  walls,  the 
distance  apart  of  the  thickness  of  the  line  to  be  drawn,  and 
which,  when  dry,  will  prevent  the  filling  ink  from  percolat- 
ing into  the  rough  paper.  In  case  of  a  very  wide  line,  the 
retaining  walls  may  have  to  be  built  up  gradually.  In 
repairing  also  it  is  necessary  to  overlap  the  correct  part  of 
the  line  sufficiently  to  include  all  that  has  been  affected  by 
the  erasing.  A  very  good  hard  drawing  paper  ought  to 
permit  several,  say  three  or  four,  corrections  over  the  same 
spot  if  skillfully  managed.  Corrections  upon  the  rough 
side  of  tracing  cloth  are  very  easily  made  with  the  ink 


54  NOTES   ON   PRACTICAL,  MECHANICAL  DRAWING. 

eraser  and  no  burnishing  is  necessary.  On  the  smooth  side, 
however,  erasing  is  difficult  and  quite  apt  to  irreparably 
injure  the  surface  of  the  cloth.  The  greatest  of  care  must 
be  used  by  rubbing  lightly  to  prevent  trouble  from  this 
cause.  A  knife  is  almost  sure  to  take  off  the  surface,  and 
if  it  does,  burnishing  will  not  repair  the  injury. 

A  knife  comes  of  service,  now  and  then  in  one  of  two 
ways,  first  to  scratch  off  the  crust  of  large  blots  or  very 
wide  lines,  without  attempting  to  remove  the  ink  entirely; 
second,  to  cut  out  an  extremely  small  spot  of  ink  or  a 
slightly  overlapping  line.  In  the  case  of  the  latter,  the 
knife  should  be  run  along  the  edge  of  the  correct  portion 
to  cut  it  away  sharply  from  the  incorrect,  then  the  error 
may  be  scratched  free  without  leaving  the  correct  line 
ragged. 

39.     General  directions  for  penciling  drawings. 
The  size  of  plates  12  inches  by  18  inches,  outside. 
Border  line  ^  inch  from  outside  edge. 

Tack  the  paper  by  the  upper  left  hand  corner,  then, 
with  T  sq.  head  against  the  left  hand  edge  of  board,  swing 
paper  into  line  with  its  upper  edge.  Next,  drawing  tight, 
tack  upper  right  hand  corner,  then  the  lower  two  corners. 

77  the  drawing  has  to  be  temporarily  removed,  draw 
short  horizontal  lines  on  each  side  of  the  sheet  and  extend- 
ing onto  the  board,  to  guide  in  replacing. 

Hold  the  T  sq.  with  the  hand  over  the  head  or  by  the 
blade  close  to  the  head.  With'  the  latter  way  the  blade  can 
be  made  to  creep  by  means  of  the  fingers  for  short  dis- 
tances across  the  paper. 

Keep  the  T  sq.  against  the  left  hand  edge  of  the  board, 
and  use  only  the  upper  edge  for  working  against. 


USE  OF  INSTRUMENTS. 


55 


Keep  the  triangles  convenient  to  the  T  sq.  and,  when 
through  using,  move  to  the  right  or  upward  from  the  blade. 

In  using  a  triangle  against  the  T  sq.  observe  the  follow- 
ing method:  Adjust  the  T  sq.  first  with  the  right  hand, 
bring  the  triangle  into  place  and  hold  with  the  fingers  of 
the  left  hand  while  the  ball  of  the  hand  rests  on  the  blade. 

FIGURE   No.   80. 


Eule  all  lines  in  pencil  and  ink  in  the  directions  shown 
in  Fig.  30.  The  vertical  lines  should  be  ruled  against  the 
left  hand  edge  of  the  triangle.  Do  not  draw  to  the  extreme 
point  of  the  triangle.  Lines  locating  points  should  cut 
each  other  as  nearly  as  possible  at  right  angles. 

The  lead  pencil  may  be  sharpened  in  one  of  two  ways, 
by  a  long,  tapering,  round  point  or  by  a  double-edged 
chisel.  Cut  the  wood  back  for  at  least  f  of  an  inch  from 
the  'end  and  leave  from  i  to  §  of  an  inch  of  lead  exposed. 
Taper  both  down  continuously  to,  if  possible,  a  slightly 
concave  form.  The  advantage  of  a  tapering  point  is  that 
it  holds  its  sharpness  for  a  longer  time,  and  again,  the 
point  is  not  thick  enough  to  cover  up  the  work  in  hand  or 
to  mislead  as  to  where  the  lead  is  marking. 


56  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 

The  double-edged  chisel  should  not  be  quite  as  wide 
across  as  the  lead  is  thick,  but  reduced  somewhat,  say  to  f 
the  diameter.  A  penknife  for  the  wood  and  emery  paper 
or  a  file  for  the  lead  will  give  the  desired  results  most 
rapidly. 

If  the  double-edged  chisel  is  used  it  should  only  be  for 
straight  away  lines,  not  for  laying  off  measurements  from 
the  rule  or  scale. 

Hold  the  pencil  nearly  perpendicularly  to  the  paper;  if 
drawing  lines  with  the  round  point,  acquire  the  habit  of 
slowly  twirling  the  pencil  during  motion,  so  that  the  point 
will  be  worn  down  in  a  conical  shape,  and  not  irregularly. 

Clean,  firm  lines,  uniform  in  thickness  and  blackness 
both  in  penciling  and  inking,  are  the  kind  which  should  be 
cultivated. 

Avoid  drawing  superfluous  lines,  lines  overrunning 
their  proper  limits  or  lines  that  are  not  to  be  inked.  If 
accidental  errors  are  made,  correct  them  with  the  eraser  at 
once. 

Lines,  which  are  to  be  dotted  in  final  drawing,  should  be 
dotted  in  pencil  so  that  no  mistake  is  made  when  inking. 

After  making  an  erasure,  clean  off  the  particles  of  dirt 
that  are  loose  on  the  paper,  for  they  interfere  with  the 
smooth  and  proper  action  of  the  other  tools.  This  is  a 
particularly  important  direction  to  observe  preparatory  to 
inking  and  when  any  alterations  are  made  during  inking. 
To  much  care  cannot  be  observed  in  freeing  the  paper  and 
all  tools  from  the  dirt  particles,  for  they  are  quite  apt  to 
get  into  the  pen  and  give  trouble. 

Successful  work  of  any  kind  must  proceed  in  a  system- 
atic and  orderly  manner.  A  system  in  penciling  cannot 


USE  OF  INSTRUMENTS.  57 

be  followed  to  advantage  entirely,  because  the  conditions 
in  the  development  of  a  drawing  vary  quite  a  little,  never- 
theless, a  general  plan  can  be  followed  when  circumstances 
permit.  The  following  is  such  a  system:—* 

System  in  Penciling. 

1.  Draw  border  lines. 

2.  Draw  match  lines  to  guide  in  replacing  the  drawing,  if  it 
is  temporarily  removed. 

3.  Block  out  space  for  title. 

4.  Block  out  space  for  bill  of  materials. 

5.  Block  out  the  views  to  be  placed  upon  the  sheet. 

6.  Draw  main  center  lines,  and  where  these  are  to  be  inked, 
they  may  be  drawn  full  light  lines. 

7.  Locate  main  lines  of  views. 

8.  Draw  small  and  inside  lines. 

9.  Put  on  dimensions  and  necessary  notes. 

4O.     General  directions  for  inking. 

To  put  ink  into  a  right  line  pen,  hold  the  pen  approxi- 
mately horizontal  with  the  kind  of  holding  usually  given  to 
a  writing  pen.  Hold  the  bottle  down  with  two  fingers  and 
with  two  fingers  lift  the  cork  out  and  touch  the  quill  end 
between  the  nibs  of  the  pen,  to  let  the  ink  run  in,  and  do 
this  over  the  bottle,  corking  it  securely  when  through.  If 
the  nibs  of  the  pen  get  ink  on  the  outside,  wipe  off  with  a 
rag. 

Hold  the  pen  perpendicularly  to  the  paper,  steadying 
the  hand  against  the  ruling  edge  with  the  last  finger  or  the 
last  two  fingers.  Place  the  first  finger  just  above  the 

•  *Coolidge  &  Freeman,  "Mechanical  Drawing." 


58  NOTES   ON   PRACTICAL  MECHANICAL  DRAWING. 

adjusting  screw  on  the  flat  part  of  the  nib,  the  thumb  just 
opposite,  and  the  second  finger  touching  the  pen  between 
the  first  finger  and  the  thumb  and  just  below  them  to  steady 
it  from  any  tendency  to  turn. 

Bear  no  weight  on  the  pen,  its  own  weight  should  be 
sufficient  to  make  the  desired  line.  If  it  does  not,  clean 
out  and  refill. 

Do  not  press  pen  against  the  ruling  edge,  as  it  will  tend 
to  close  the  nibs. 

Make  all  lines  by  a  continuous  motion  of  the  pen. 

Do  not  stop  on  a  line  to  see  where  the  rest  of  the  line  is 
to  go.  If  it  is  absolutely  necessary  to  stop  in  any  case, 
even  for  a  moment,  lift  the  pen  from  the  paper.  Also, 
when  stopping  in  this  way,  take  the  further  precaution  to 
move  the  ruling  edge  away  from  the  wet  line. 

When  requiring  refilling,  clean  the  pen  out  thoroughly 
inside  and  out.  It  is  well  to  cultivate  the  habit  of  doing 
this  early,  making  it  invariable,  for  a  pen  clogged  with  ink 
is  likely  to  give  trouble.  Use  the  nails  of  the  thumb  and 
first  finger  successively,  covered  by  one  thickness  of  rag, 
and  it  will  be  found  easy  to  clean  one-half  of  a  blade  with 
one  finger  and  the  other  half  with  the  other,  and  the 
remaining  blade  by  turning  the  pen  over  and  repeating  the 
operation.  Four  wipes  generally  clean  sufficiently. 

//  the  pen  gives  any  trouble  in  marking  at  any  time  it  is 
safest  to  empty,  clean  and  refill. 

The  weight  of  an  ink  line  on  a  drawing  should  be  such 
that  it  will  show  clearly  the  form  within  the  maze  of 
dimension  lines,  etc.,  that  it  will  blue  print  readily,  giving 
an  equally  clear  impression  throughout,  and  that  all  annoy- 
ance is  removed,  due  to  the  likelihood  that  the  line  will 


USE  OF  INSTRUMENTS.  59 

FIGURE    No.    81. 


/•  ofc? 


break,  through  any  obstructed  flow  from  the  pen.  In  Fig. 
31  are  shown  suitable  conventions  to  use  on  a  drawing,  as 
well  as  the  proper  weight  of  line. 

System  in  inking  is  more  imperative  than  in  penciling 
owing  to  the  trouble  of  changing  tools  and  waiting  for  ink 
to  dry.  A  general  plan  which  will  be  found  useful  follows : 

System  in  inking. 

1.  Ink  all  small  circles  and  arcs  of  circles  with  the  bow  pen. 

2.  Ink  larger  circles  and  arcs  with  the  compass. 

3.  Ink  irregular  curves  with  curve  ruler. 

4.  Ink  all  horizontal  lines  with  the  T  sq. 

5.  Ink  all  vertical  lines  with  the  triangle  resting  on  the  T 
sq.  edge. 

6.  Ink  all  45°,  30°  and  60°  lines  in  groups  and  in  order. 

7.  Ink  other  oblique  lines  not  at  the  above  angles. 

8.  Section  lining. 

9.  Dimensioning. 

10.  Surface  tinting  and  shading. 

11.  Lettering  and  descriptive  matter. 


60  NOTES   ON   PRACTICAL  MECHANICAL,  DRAWING. 

In  large  complicated  drawings,  treat  a  small  portion 
of  the  sheet  at  a  time  complete  with  one  tool  until  the 
whole  has  been  covered.  Some  authorities  advocate  draw- 
ing center  lines  first,  and  it  is  also  a  good  method. 

Section  lining  and  dimensioning  may  conveniently 
change  places  in  the  series  where  dimensions  do  not  have 
to  be  written  across  sectioned  surfaces. 

41.  A  drawing  should  be  cleaned   after  all  inking  is 
finished.    A  soft  rubber  will  clean  off  the  dirt  well,  but  it 
is  not  sufficient  for  erasing  superfluous  construction  lines. 
Take  the  latter  out  carefully  with  a  harder  eraser  so  as  not 
to  injure  the  ink  lines. 

42.  Handling  of  the  compass,  dividers  and  bows. 

The  compass  is  for  describing  circles  and  measuring 
angles,  and  also  for  transferring  measurements  from  one 
place  to  another. 

The  dividers  are  used  to  approximately  subdivide 
linear  distances  and  for  transferring  measurements  from 
one  place  to  another.  It  is,  many  times,  a  more  conven- 
ient tool  for  doing  these  things,  and  one  of  the  habits  to 
cultivate  is  to  minimize  the  use  of  the  dividers.  It  is  an 
excellent  tool  in  its  place,  but  it  is  not  as  safe  to  depend 
upon  as  the  scale. 

In  changing  the  marking  legs  of  the  compass,  use  care 
to  pull  or  push  the  attachment  longitudinally  of  the  leg, 
and  not  to  twist  it  or  move  it  laterally,  it  might  strain  the 
members.  The  instrument  is  easily  injured,  and  accuracy 
of  action  is  necessary. 

The  needle  point  of  the  compass  should  have  a  shoulder 


USE  OF  INSTRUMENTS.  61 

on  it  to  prevent  sticking  too  deep  in  the  paper;  it  should 
be  adjusted  to  fit  the  pen  attachment  and  always  be  kept 
so.  In  working  with  the  pencil  leg  then,  and  as  it  wears 
down,  extend  the  lead  to  meet  properly  the  needle  point 
adjustment.  The  pencil  in  the  compass  should  be  sharp- 
ened always  to  the  double-edged  chisel. 

The  proper  position  for  the  needle  point  is  slightly  in 
advance  of  the  marking  point,  depending  upon  the  degree 
of  sharpness  and  the  length  of  the  point.  At  no  time 
should  the  point  more  than  hold  in  the  paper.  And  when 
stuck  in  to  this  degree,  the  bisector  of  the  angle  of  the  com- 
pass legs  should  be  perpendicular  to  the  line  connecting 
the  two  points.  This  is  very  important  in  making  small 
circles. 

The  compass  should  be  held  with  one  hand  only,  for 
reasons  apparent  after  experience. 

To  open  the  compass  at  first,  press  the  thumb  and  first 
finger  against  the  bevelled  portion  near  the  head. 

To  hold  the  compass  when  opened,  control  the  needle 
point  leg  with  the  thumb  and  third  finger,  the  marking  leg 
with  the  first  and  second  fingers,  held  generally,  the  former 
upon  the  outside,  the  latter  upon  the  inside  of  the  leg,  so 
as  to  move  the  leg  in  and  out  with  a  controlled  motion. 

The  tightness  of  the  head  should  be  just  sufficient  to 
hold  the  compass  in  place  during  use;  such  an  adjustment 
will  not  render  it  difficult  to  change  the  angle  between  the 
legs  easily  with  the  fingers  as  described. 

If  the  hand  is  unsteady,  it  may  be  found  convenient  to 
use  one  hand  for  putting  the  needle  point  in  the  proper 
center,  either  by  taking  hold  of  the  end  of  the  needle  point 
leg  or  by  resting  the  leg  against  the  finger  while  putting  it 
into  place ;  the  latter  is  the  better  way. 


NOTES   ON   PRACTICAL  MECHANICAL  DRAWING. 

Curves  should  be  drawn  continuously  and  always  clock- 
wise. In  drawing  a  complete  circle,  start  the  marking 
point  at  the  lowest  part  of  the  circle,  or  even  a  little  to  the 
right,  and  it  will  be  found  possible  to  swing  the  whole 
circle  without  change  of  handling,  by  rolling  the  head  in 
the  fingers  during  rotation.  It  should  not  be  necessary  to 
change  the  handling  at  any  time,  or  the  position  of  the 
hand  on  the  instrument.  Held  correctly,  it  should  always 
be  ready  for  drawing.  It  is  a  very  common  fault  to  hold 
the  compass  with  two  hands. 

It  should  be  held  so  that  the  head  is  slightly  in  advance 
of  the  marking  point  in  the  direction  in  which  the  curve  is 
being  made,  to  aid  the  marking  point  to  remain  in  contact 
with  the  paper.  But  do  not  bear  any  more  pressure  on 
either  leg  than  is  necessary  to  make  the  curve  and  to  keep 
the  needle  point  in  contact  with  the  paper;  in  ink  work, 
the  weight  of  the  instrument,  as  in  the  case  of  the  ruling 
pen,  should  be  sufficient  to  make  the  desired  line. 

Do  not  overlap  a  circle  in  inking;  there  is  a  chance  of 
a  change  of  adjustment,  and  even  if  this  is  not  the  case,  it 
is  likely  that  a  line  twice  drawn  over  will  spread  out 
making  a  noticeable  junction. 

The  hairspring  attachment  put  on  some  compasses 
and  dividers  has  merits  in  enabling  one  to  make  a  very 
delicate  change  of  adjustment,  but  the  author  thinks  the 
value  of  this  feature  is  very  much  over  estimated,  for,  with 
experience,  comes  sufficient  skill  that,  handled  as  above 
described,  the  desired  adjustments  are  made  more  rapidly 
than  they  could  be  by  a  hairspring  attachment.  Of  the 
two  instruments,  however,  the  hairspring  is  of  more  value 
upon  the  compass  than  upon  the  dividers. 


USE  OF  INSTRUMENTS.  63 

For  large  circles,  bend  the  legs  of  the  compass  at  the 
joint  provided  so  that  they  come  down  perpendicularly  to 
the  paper. 

A  lengthening  bar  is  used  for  circles  beyond  the 
capacity,  ordinarily,  of  the  compass,  but  it  is  an  inconven- 
ient thing,  makes  an  unsteady  tool,  and  if  much  work  is  to 
be  done  on  large  radii  it  is  well  to  use  a  beam  compass, 
built  especially  for  this  purpose. 

The  dividers  are  held  in  the  same  manner  as  the 
compass.  If  a  given  distance  is  to  be  divided  into  a  certain 
number  of  equal  parts  that  do  not  correspond  to  any  scale 
divisions,  the  dividers  can  be  used  to  do  it  by  successive 
approximations.  In  stepping  off  such  equal  spaces,  the 
tool  should  be  swung  alternately  over  and  under.  More- 
over, but  slight  pressure  should  be  exerted  on  the  tool,  so 
that  the  points  make  no  noticeable  hole  in  the  paper. 

To  locate  a  pick  of  the  divider  leg  for  further  reference, 
put  a  small  free-hand  circle  about  the  point,  not  much  over 
a  sixteenth  of  an  inch  in  diameter;  this  calls  attention  to 
the  region  in  which  the  point  lies.  Large  holes  in  a  draw- 
ing are  unsightly  and  are  really  inaccurate. 

The  bow  instruments  are  very  convenient,  small  and 
accurate  tools  for  doing  the  same  kind  of  things  that  the 
compass  and  dividers  will  do.  The  adjustment  of  needle 
to  marking  point  in  the  bow  pen  and  pencil  should  be  even 
more  carefully  made  than  in  the  compass,  because  of  the 
small  circles  for  which  they  are  used.  On  account  of  their 
accuracy  and  positive  adjustment,  the  bows  in  practical 
work  are  used  wherever  they  can  be,  but  since  there  is 
nothing  distinctive  to  be  learned  about  them,  the  beginner 
is  advised  rather  to  favor  the  use  of  the  latter  so  that  he 


64  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 

may  get  as  much  practice  with  them  as  possible,  and 
acquire  the  proper  handling,  which  does  not  generally 
come  naturally  at  first. 

The  small  circles  upon  commercial  drawings  are  not 
infrequently  omitted  in  penciling,  only  the  centers  being 
located,  but  a  caution  is  extended  to  the  beginner  not  to 
resort  to  this  form  of  short  cut,  but  to  pencil  in  everything 
very  completely  and  accurately.  The  omissions  of  con- 
struction should  be  left  to  the  judgment  of  the  skillful 
draftsman. 

If  a  decided  change  is  to  be  made  in  the  adjustment  of 
the  bows,  it  is  less  wear  on  the  instrument  and  also  more 
economical  of  time  to  take  the  strain  off  the  legs  by  press- 
ing them  together  with  one  hand  while  the  thumb  screw  is 
twirled  around  with  the  other  until  near  the  proper 
adjustment. 

43.  The  use  of  the  irregular  curve:  The  irregular  curves 
are  those  which  cannot  be  drawn  accurately  with  the  com- 
pass. They  must  be  plotted  by  points  and  the  latter  joined 
by  a  smooth  curve  made  with  the  curved  ruler  or  " curve" 
as  it  is  called. 

The  curve  can  be  drawn  best  at  first  free-hand  and 
then  copied  with  the  "curve." 

The  correct  shape  for  a  "curve"  is  of  importance.  The 
best  is  one  which  has  the  fewest  and  simplest  curves  in 
one  tool,  as  the  spiral  form  for  example. 

The  "curve"  should  be  applied  to  the  points  plotted 
with  the  direction  of  the  change  of  curvature  the  same  in 
both. 

The  drawn  curve  should  be  as  unbroken  as  the  theoret- 


USE  OF  INSTRUMENTS.  65 

ical  curve,  and  its  execution  is  not  easy  at  first.  To  insure 
matching  the  curve,  apply  the  "curve"  to  at  least  three 
points,  more  if  possible,  then  draw,  not  as  far  as  the  ruler 
seems  to  match  the  curve  but  a  little  short  of  it,  the 
amount  depending  upon  how  rapidly  the  ruler  departs 
from  the  curve  to  be  drawn  at  the  last  discernable  point. 
Again,  in  moving  to  the  next  segment,  match  the  ruler  to 
the  part  already  drawn  so  that  it  corresponds  with  it  for 
an  appreciable  distance  back  of  the  last  point  drawn  to. 

To  connect  the  segments  of  the  line  accurately,  head  the 
pen  first  to  make  a  perfect  alignment,  then  start  to  move 
on  the  line,  or  if  drawing  up  to  a  line,  and  just  before 
reaching  it,  tilt  the  pen,  if  necessary,  to  bring  it  into  the 
ink  line  correctly,  but  do  not  overlap. 

Keep  the  blades  of  the  pen  at  all  tunes  tangent  to  the 
ruling  edge,  but  do  not  work  on  the  under  side  of  the 
"curve." 


CHAPTER  V. 
WORKING  DRAWINGS. 

44.     Orthographic  projection  and  working  drawing. 

Orthographic  projection  is  the  language  in  which 
working  drawings  are  written,  but  a  dimensioned 
orthograghic  projection  of  anything  does  not  necessarily 
constitute  a  working  drawing  of  that  thing. 

A  working  drawing  must  be  simple  and  plain  in  its  fea- 
tures, easy  to  be  interpreted,  yet  explicit.  For  if  one  view 
of  a  piece  will  suffice  to  tell  a  workman  how  to  make  it, 
only  the  one  view  need  be  made.  On  the  other  hand, 
however,  more  views  may  be  required  in  the  working 
drawing  than  are  required  in  orthographic  projection,  for 
sometimes  assembly  views  are  needed  to  show  relation  of 
all  parts  and  detail  drawings  of  each  component  part  in 
addition.  The  principles  of  orthographic  projection  are 
frequently  violated  in  working  drawings  wherever  modifi- 
cation will  aid  in  legibility  or  economy  of  time  in  drawing. 

There  is  no  way  to  formulate  this  difference  between 
the  two  under  rules  for  there  are  no  fixed  ones.  The 
draftsman  should  place  himself  in  the  position,  in  imagina- 
tion, of  the  one  who  is  going  to  construct  from  his  drawings, 
and  in  that  way  arrive  at  a  conclusion  as  to  what  would 
be  desirable  in  the  way  of  views.  Unless  the  draftsman 
does  this,  he  is  apt  to  economize  time  and  effort  at  the 
expense  of  the  workman's  time.  From  the  workman's 
standpoint,  many  times,  drawings  are  not  explanatory 


WORKING  DRAWINGS.  67 

enough;  he  will  want  them  too  elaborated  with  directions. 
A  mean  of  these  two  has  to  be  struck. 

45.  A  set  of  working  drawings  in  its  completest  form, 
consists  of  diagrams,  assembly  views,  details,  sections 
and  bill  of  materials. 

A  diagram  is  a  drawing  which  is  first  made  to  deter- 
mine upon  the  arrangement  or  lay  out  of  the  various  parts. 
Upon  this  lay  out,  also,  may  depend  the  character  of  the 
forms,  so  that  this  is  an  additional  requirement  for  its 
being  made  first.  The  diagram  shows,  further,  the 
number  of  the  various  elements  of  the  group.  As  one 
illustration  of  this  kind  of  drawing  can  be  mentioned  a 
layout  for  piping,  showing  the  number  of  elbows,  tees, 
valves,  etc. 

In  a  diagram  the  briefest  indication  of  shape  is  given, 
and  not  infrequently  special  conventional  forms  are  used 
to  stand  for  the  more  intricate  actual  forms.  In  piping, 
for  instance,  a  valve  is  represented  by  two  short  lines 
perpendicular  to  and  crossed  by  each  other,  one  per- 
pendicular to  the  line  of  piping  and  standing  for  the 
entire  valve,  the  other  parallel  to  the  line  of  the  piping  and 
standing  for  the  handle. 

Another  illustration  of  the  diagram  is  an  outline  of  a 
machine  composed  of  the  main  lines,  together  with  the 
usual  center  lines.  Perhaps,  in  this,  the  relation  of  some 
of  the  moving  parts  is  shown.  These  may  be  represented 
by  heavy  lines  coinciding  with  the  center  lines  of  the 
members  for  which  they  stand,  as  in  a  Corliss  engine  valve 
gear  diagram. 

The  assembly  drawing  shows  the  entire  subject  to  be 


68  NOTES   ON   PRACTICAL,  MECHANICAL  DRAWING. 

treated.  It  may  not  show  all  the  features,  or  parts,  only 
the  principal  ones ;  but  it  gives  certain  facts  not  available 
in  any  other  way.  It  shows  the  size  of  the  whole,  the 
place  for  the  different  component  parts,  and  the  relation 
between  these,  together  with  certain  desirable  chief  dimen- 
sions. The  minor  features,  such  as  bolts,  nuts,  keys,  set 
screws,  etc.,  are  left  off.  Perhaps  their  place  will  be  indi- 
cated by  center  lines;  perhaps, not  even  that.  In  fact,  the 
assembly  drawing  may  be  more  or  less  in  the  form  of  a 
diagram. 

The  details  are  made  together  upon  a  sheet  of  details, 
or  each  may  be  made  on  a  separate  sheet  for  the  different 
workmen,  according  to  the  process  through  which  the 
parts  are  to  be  put.  There  are  details,  for  example,  for  the 
pattern  maker,  the  blacksmith  or  the  machinist.  The 
dimensions  put  on  these  and  the  general  treatment  will  be 
that  of  interest  to  the  particular  workman  handling  them. 
Sometimes  the  detail  drawings  are  made  complete  enough 
in  all  respects  to  answer  for  the  several  above  mentioned 
requirements. 

46.  Sections  are  made  many  times  to  save  the  drawing 
of  details.    A  section  in  its  simplest  form,  means  to  cut 
anything  as  with  a  saw  and  to  show  by  some  conventional, 
or  commonly  understood  means,  the  plane  of  the  cut  and 
what  lies  beyond  this  plane  when  looking  perpendicularly 
at  it.    The  treatment  of  sections  will  be  taken  up  a  little 
later. 

47.  The  bill  of  materials   is  a   tabulation  of  the  stock 
required,  the  number  and  character  of  the  pieces  needed. 


WORKING  DRAWINGS. 

To  be  specific,  it  is  composed  of:  (a.)  An  identification 
mark  as  a  number,  which  may,  by  its  denomination,  indi- 
cate the  material.  (&.)  Name  of  the  part,  (c.)  Number 
of  the  pieces  needed  to  make  one  of  the  entire  subject. 
(d. )  Name  of  material,  if  the  identification  is  not  complete 
as  above,  (e.)  Further  general  descriptive  matter,  like 
pattern  number,  dimensions  of  the  rough  stock,  method  of 
casting,  etc.  In  very  small  subjects  it  may  not  be  made  a 
separate  tabulation,  but  written  near  the  separate  parts. 
In  other  cases  it  may  be  a  tabulation  in  one  corner  of  the 
sheet  containing  the  pieces  detailed.  When  very  com- 
plicated drawings  are  dealt  with,  it  may  be  accorded  a 
separate  sheet  or  sheets. 

48.  Working  drawings  may  violate  the  rules  of  ortho- 
graphic projection:— Projection  is  the  theoretical  side, 
working  drawings  are  the  practical  application  of  theory. 
Custom  has  santioned  certain  practices,  more  or  less 
universal,  for  making  drawings  more  explanatory  with  less 
labor,  while  there  are  innumerable  short  cuts,  etc.,  adopted 
by  different  establishments,  known  only  to  the  individuals 
having  use  for  them.  Some  few  of  the  general  principles 
which  may  be  followed  will  be  here  touched  upon : 

*  (a.)  "That  in  each  separate  view,  whatever  is  shown 
at  all  should  be  represented  in  the  most  explanatory 
manner." 

(b.)  "That  which  is  not  explanatory  in  any  one  view 
may  be  omitted  therefrom,  if  sufficiently  defined  in  other 
views." 


*  McCord  Mech.  Draw.  Part  II,  Page  8. 


70  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 

(c.)  "The  proper  position  of  a  cutting  plane  is  that 
by  which  the  most  information  can  be  clearly  given." 

(d.)  "It  is  not  necessary  to  show  in  section  every- 
thing which  might  be  divided  by  a  cutting  plane." 

(e.)  "Whatever  lies  beyond  a  cutting  plane  may  be 
omitted  when  no  necessary  information  would  be  conveyed 
by  its  representation." 

The  views  necessary  to  show  a  subject  do  not  follow 
the  conventional  ones  of  projection,  for  if  one  view  is 
sufficient  to  tell  the  workman  all  the  facts,  more  are  super- 
fluous; for  example,  one  view  of  a  bolt  is  all  that  is  needed 
when  the  bolt  is  standard.  The  certainty  that  the  work- 
man could  not  make  anything  else  from  the  drawings  than 
the  thing  intended  is  the  controlling  condition. 

When  two  pieces  differ  only  in  being  rights  and  lefts, 
it  is  usually  not  necessary  to  draw  but  one  of  them,  making 
an  explanatory  note  on  the  drawing  that  two  are  wanted, 
one  right  and  one  left. 

A  section  and  an  elevation  are  sometimes  combined  on 
the  one  view  by  superimposing  the  lines  of  the  elevation 
over  those  of  the  section.  This  saves  one  view. 

Lines  coming  very  close  when  drawn  to  scale  should  be 
separated,  that  is,  the  scale  exaggerated,  or  else  one  line 
left  out. 

In  gears,  a  few  teeth,  perhaps  only  one,  are  drawn  out 
in  full ;  the  remainder  are  indicated  by  dotted  circles  for 
their  crowns  and  for  their  roots,  the  pitch  circle  being  a 
dash  and  dot  line,  or  the  usual  convention  for  center  line, 
or  it  may  even  be  made  a  solid  line. 

In  sectioned  views,  continuity  of  material  is  not  inter- 


WORKING  DRAWINGS.  71 

fered  with  by  the  introduction  of  minor  elements  in  the 
plane  of  the  section.  They  are  either  left  out  or  put  in 
dotted. 

Sometimes  in  the  drawing  of  one  part  of  an  object, 
which  it  is  particularly  desired  to  show,  there  are  other 
parts  connected  with  it  which  may  be  rendered  in  dotted 
lines  to  help  show  the  connection  of  them  all. 

And  so  illustrations  may  be  multiplied,  but  it  is  not 
necessary  to  go  farther.  The  different  illustrations  in  the 
book  will  show  some  of  the  short  cuts.  Judgment  and 
experience  will  open  up  others  to  the  thoughtful  drafts- 
man, and  he  will  even  then  occasionally  find  that  there  are 
opportunities  for  him  to  improve  on  past  experience. 

49.    The    development    and    arrangement    of    working 
drawings. 

In  beginning  a  set  of  working  drawings  of  a  subject 
which  is  entirely  new  in  design,  it  is  possible  that  the  small 
features  will  be  designed  first,  and  the  assembly  drawings 
of  parts,  or  of  the  whole,  made  afterwards,  so  there  can  be 
no  rule  for  the  order  in  which  drawings  are  made. 

Differences  in  manufacture  and  in  the  subject 
control  the  method  of  development  and  arrangement. 
Principles  cannot  be  laid  down  applicable  to  all  cases. 
Some  one  problem  may  be  considered  somewhat  in  detail, 
and  will  serve  to  show  how  it  is  done,  and  about  the  best 
illustration  that  can  be  taken  is  an  academic  exercise,  a 
problem  which  would  be  given  a  student  in  drawing,  that 
of  making  a  set  of  working  drawings  of  a  model  of  a 
simple  steam  engine. 

Determine  the  chief  dimensions  or  size  of  the  whole, 


72  NOTES   ON   PRACTICAL  MECHANICAL  DRAWING. 

and  choose  such  a  scale  which  will  properly  present  the 
assembly  drawings,  a  plan,  elevation  and  end  view,  upon 
one  sheet  without  overcrowding  the  sheet.  Next,  take  in 
turn  the  various  parts,  and  make  the  necessary  working 
drawings  of  each.  It  is  best  to  take  a  survey  of  the  size  of 
the  largest  piece  and  of  the  smallest,  and  see  of  what  size 
they  can  be  conveniently  made,  using  only  one  scale  for 
all.  Lay  out  the  projections  of  the  larger  pieces  first,  and 
proceed  toward  the  smaller,  and  so  on. 

Details  of  construction:  Before  any  drawing  is  done, 
a  list  should  be  made  of  all  the  features  needing  to  be 
detailed,  and  the  number  and  kind  of  views  required  of 
each,  a  written  list  is  preferable. 

The  arrangement  of  the  sheets  should  next  be  decided 
upon.  In  practical  work  different  sized  sheets  are  used  for 
the  different  parts  of  the  subject;  frequently,  the  assembly 
views  will  be  made  upon  a  relatively  large  sized  sheet,  the 
main  details  on  a  second  or  medium  sized  sheet,  and  the 
smallest  parts  on  small  sheets.  Small  parts  require, 
generally,  finishing  or  machine  work,  and  it  is  more  con- 
venient in  the  shop  to  handle  the  small  sheets,  mounted  as 
they  often  are,  on  board,  or  some  stiff  backing,  and  var- 
nished. 

To  get  the  best  arrangement,  a  free  hand  sketch  treat- 
ment should  be  used  first,  that  is,  to  an  approximate  scale, 
sketch  roughly,  by  very  light  lines,  the  space  to  be  occu- 
pied by  each  and  all  of  the  views.  This  will  permit  of  an 
adjustment  in  the  arrangement,  if  it  does  not  at  first 
promise  to  be  good. 

Begin  the  careful  drawing  of  the  details  first,  leaving 
the  assembly  drawings  until  later,  as  the  best  interpreta- 


WORKING  DRAWINGS.  73 

tion  and  accuracy  can  be  reached  in  working  the  assembly 
from  the  details. 

Draw  the  views  of  the  bed  of  the  engine  first.  Do  not 
begin  at  the  top  or  bottom,  and  build  steadily  down  or  up 
until  finished,  but  lay  out  the  chief,  or  the  over  all  sizes, 
then  the  next  smaller,  and  so  on,  to  the  smallest  parts  last; 
also,  drawing  not  one  view  at  a  time,  but  the  several  of  the 
set;  the  same  features  recurring  in  the  several  views  should 
be  treated  in  them  all,  so  that  there  should  be  harmony  of 
parts. 

If  a  view  can  be  developed  by  projection  from  another, 
it  is  better  to  do  so  than  to  use  the  scale  and  lay  it  out 
independently,  for  it  saves  time.  But  the  scale  relation 
must  be  kept  in  mind  and  discrepancies  noted. 

The  place  on  the  sheet  for  the  different  views  should  be 
appropriate  and  follow  a  certain  system.  Large  details 
should  be  put  on  a  sheet  by  themselves,  or  else  along  the 
upper  part  of  the  sheet,  or  at  the  left  hand  side.  The 
next  smaller  parts  should  be  put  below  the  first,  or  to  the 
right,  and  so  on,  so  that  the  smallest  parts  are  shown 
along  the  bottom,  or  along  the  right  hand  edge  of  the 
sheet. 

Related  parts  may  be  in  protectively,  related  positions, 
provided  the  subject  admits  of  it,  or  while  not  in  project- 
ively,  related  positions,  they  may  be  so  intimately  related 
on  the  drawing  that  the  connection  is  apparent  at  a  glance. 
For  illustration:  A  connecting  rod— showing  the  rod  at 
the  top— may  have  the  straps  to  the  left  and  right  of  the 
rod  as  if  they  had  just  been  slipped  off,  their  center  lines 
coinciding  with  that  of  the  rod ;  the  brasses  may  be  shown 
also  to  the  right  and  left  of  the  straps  as  if  they  had  been 


74  NOTES   ON  PRACTICAL,  MECHANICAL  DRAWING. 

removed  by  simply  sliding  along  their  center  lines  coin- 
ciding with  that  of  their  position  in  the  straps ;  finally,  the 
keys,  and  bolts,  etc.,  may  be  put  in  the  lower  part  of  the 
sheet  in  any  convenient  place,  arranged  so  that  the  left 
hand  bolts,  etc.,  belong  at  the  left  hand  end  of  the  rod, 
and  those  at  the  right,  to  the  right  hand  end  of  the  rod. 
This  may  be  seen  illustrated  in  diagram,  Fig.  32. 

Another  logical  and  perhaps  better  arrangement  is 
shown  in  diagram,  in  Fig.  33.  Here  the  principle  is  fol- 
lowed of  placing  parts  of  a  kind  together,  disregarding  their 
exact  position  in  the  subject.  The  straps  of  both  ends  are 
put  together  at  the  left,  but  the  upper  one  belongs  to  the 
left  hand  end  of  the  rod,  and  the  lower  one  to  the  right 
hand  end  of  the  rod,  a  certain  convention  of  sequence 
which  is  quite  common.  Similarly,  the  brasses  are  placed 
at  the  right  with,  again,  the  left  hand  brass  above  and  the 
right  hand  one  below.  The  last  mentioned  plan  of  Fig.  33 
is  the  best  in  general. 

If  the  engine  were  complex,  probably  the  connecting 
rods  would  be  put  on  a  sheet  with  the  eccentric  rods,  or 
other  long  turned  members,  the  brasses  all  together  on  a 
sheet  by  themselves,  and  the  straps  also.  Even  here, 
however,  the  rods  for  the  high  pressure  (H.P.),  low 
pressure  (L.P.),  and  intermediate  pressure  (I. P.),  would 
follow  each  other  down  or  across  the  sheet  in  a  certain 
sequence,  which  would  be  the  same  as  that  on  the  sheet  of 
brasses  and  straps,  etc.  It  is  evident  that  such  an  arrange- 
ment would  aid  materially  in  reading  the  drawings  and 
finding  what  is  wanted. 

If  several  parts  of  the  engine  are  put  on  a  sheet,  the 
groups  of  drawings  of  them  should  be  separated  by  a  little 


WORKING  DRAWINGS. 


75 


NOTES  ON  PRACTICAL,  MECHANICAL,  DRAWING. 


^ 
I 


3          O 


O 


WORKING  DRAWINGS.  77 

more  space  than  the  several  views  of  a  part,  so  that  the 
identity  of  the  different  things  is  not  confused. 

Parts  which  have  to  be  made  upon  the  same  machine, 
or  by  similar  processes,  are  often  collected  on  a  separate 
sheet  by  themselves;  for  example,  there  may  be  a  sheet  of 
bolts  alone,  of  screws,  of  forcings  and  of  castings;  but  this 
is  done  only  where  a  large  number  of  parts  is  wanted,  and 
where,  moreover,  processes  of  manufacture  have  become 
somewhat  systematized. 

If  it  takes  more  than  one  sheet  to  make  a  set  of 
drawings,  keep  each  sheet  as  far  as  possible  self  contained, 
even  though  on  some  sheets  there  may  be  waste  room. 
The  economy  of  space  profits  little,  nor  the  even  distri- 
bution of  views  over  the  sheet  unless  it  can  be  done  with- 
out any  sacrifice. 

5O.  Drawing  to  scale  is  necessary  where  forms  dealt 
with  are  larger  than  the  ordinary  sized  drawing  paper  will 
take  full  size.  It  is  no  hindrance  to  the  workman,  because 
he  takes  his  sizes  from  those  specified  on  the  drawing  and 
is  generally  not  permitted  to  use  anything  else. 

There  are  a  number  of  kinds  of  scales  made,  divided 
broadly  into  civil  engineer's  and  architect's  or  mechanical 
engineer's  and  are  either  flat  or  triangular.  The  civil 
engineers'  scale  is  one  in  which  the  divisions  of  inches  are 
by  even  decimals,  tenths,  twentieths,  thirtieths,  etc.  The 
flat  scale  may  contain  two,  four  or  eight  scales,  according 
to  the  way  in  which  its  edges  are  divided,  and  is  a  conven- 
ient tool  because  of  its  flatness.  The  triangular  scale 
usually  contains  twelve  different  scales,  and  because  of  its 
wide  range  is  probably  the  favorite. 


78  NOTES  ON  PRACTICAL  MECHANICAL  DRAWING. 

In  engineering,  when  scale  is  mentioned,  it  means  so 
many  inches  or  fractions  of  an  inch  will  stand  for  a  foot  of 
the  actual  thing  drawn.  To  take  a  concrete  case:  On 
one  face  of  the  triangular  scale,  the  edge  is  divided  into 
3-inch  major  divisions,  identified  by  numbers  on  the  flat 
surface,  the  edge  is  also  divided  into  1^  inch  minor  divis- 
ions, identified  by  numbers  on  the  curved  part  of  the  scale. 
At  the  right  a  three  inch  space  is  divided  into  twelve 
major  divisions  to  stand  for  inches  and  each  of  these  again 
into  eighths.  At  the  left  a  1J  inch  space  is  similarly 
divided,  except  that  each  space  standing  for  one  inch  is 
divided  into  quarters.  Hence,  by  overlapping,  we  have 
two  scales  to  an  edge.  To  lay  off  a  dimension  with  the 
three  inch  scale  we  read  the  even  feet  to  the  left  of  the 
zero  mark  and  the  inches  or  fractions  to  the  right. 

Points  to  be  observed  in  the  handling  of  the  scale: — 
It  should  never  be  used  as  a  rule. 
With  a  sharp  and  round  pointed  pencil,  make  a  short 

straight  stroke  at  the  scale  division,  and  perpendicular 

to  the  edge,  about  one  thirty-second  of  an  inch  long. 
Transfer  measurements  with  the  scale  where  possible,  that 

is,  indicate  the  size  by  scale  measurement,  then  set  the 

compass  to  the  marks  made  if  it  is  necessary  to  strike 

an  arc  of  that  radius. 
Successive    measurements    should  be  laid    off  with   one 

setting  of  the  scale  where  possible. 

The  problems  arising  in  the  use  of  the  architect's  or 
mechanical  engineer's  scale  group  themselves  under  three 
heads. 


WORKING  DRAWINGS.  79 

(1.)  To  make  a  drawing  a  given  fraction  of  the 
original  in  size. 

(2.)  Given  the  scale  used  to  determine  the  fraction 
of  size  which  the  drawing  is  of  the  original. 

(3.)  Given  the  size  of  the  space  in  which  a  drawing 
must  be  made  to  fit,  to  determine  the  scale  to  be  used  to 
get  this  reduction  from  the  original. 

(1.)  To  illustrate:  Suppose  it  is  desired  to  make  a 
drawing  one-quarter  the  size  of  the  original;  ix!2  =  3; 
therefore  3  inches  is  the  scale  or  size  per  foot  to  be  used. 

(2.)  To  illustrate:  Suppose  a  drawing  is  made  to  a 
scale  of  one-quarter  of  an  inch  to  the  foot,  then,  as  i  :  12 
so  the  drawing  is  to  the  original  or  TT  the  size. 

(3.)  To  illustrate:  Suppose  a  subject  3  feet  long  is 
to  be  reduced  in  drawing  to  1^  inches,  the  length  being  the 
determining  dimensions,  then  1£  :  36  x  12  =  £,  or  the  scale 
is  \  inch  to  the  foot. 

When  problems  do  not  come  out  as  even  as  these,  the 
nearest  available  scale  is  taken.* 

There  is  a  special  and  popular  form  of  scale  made  for 
mechanical  engineering  work  which  differs  in  divisions 
from  the  ordinary  scale.  The  inch  and  not  the  foot  is 
made  the  unit  for  subdivisions.  The  scales  shown  are  for 
half  size,  quarter  size  and  eighth  size.  The  half  size,  for 
example,  has  a  half  inch  divided  again  into  halves, 


*A  very  common  error  arises  from  mixing  up  scale  with  fraction.  A  quarter 
scale  drawing  means  a  drawing  made  i  Inch  to  one  foot,  while  a  i  size  drawing 
means  a  drawing  made  8  Inches  to  a  foot.  In  other  words  when  we  speak  of  a 
fractional  size  we  do  not  mean  that  fraction  as  the  scale  but  that  fraction  of  12 
Inches,  the  foot  being  the  unit. 


80  NOTES   ON   PRACTICAL  MECHANICAL  DRAWING. 

quarters  and  eighths,  to  represent  those  fractions  respec- 
tively of  an  inch. 

Sometimes  a  purely  arbitrary  and  exact  scale  is 
required,  and  has  to  be  constructed.  It  can  be  readily 
done  by  a  method  based  upon  the  geometrical  principle 
that  lines  parallel  to  one  side  of  a  triangle  divide  the 
adjacent  sides  in  proportional  parts. 

The  civil  engineer's  or  decimated  scale  is  mainly  a 
scale  for  use  when  the  reduction  is  relatively  large  so  that 
from  10  to  100  feet  will  be  represented  by  an  inch,  for  it  has 
divisions  of  lOths,  20th s,  30ths,  40ths  and  50ths  of  an  inch. 
It  can  also  be  used  in  the  same  way  as  the  mechanical 
engineer's  scale.  To  illustrate:  The  twentieths  scale 
can  be  used  for  i  inch  to  the  foot,  five  divisions  being 
equivalent  to  one  foot,  two  and  one-half  to  six  inches,  etc. 
The  thirtieths  can  be  used  for  six  inches  to  the  foot,  five 
divisions  then  equalling  one  inch. 

51.  A  section,  or  cut,  through  the  whole,  or  part,  of  any 
subject  is  conventionally  represented  by  covering  the 
sectioned  parts  with  evenly  spaced  parallel  lines.  They 
are  not  intended  to  represent  or  suggest  a  tinted  surface, 
hence,  to  distinguish  it  as  a  sectioned  surface  the  hatching 
lines,  as  they  are  called,  are  ruled  diagonally  of  the  edges 
of  rectangular  forms.  Contiguous  parts  are  section  lined 
in  opposite  directions.  In  any  position  whatever  of  the 
contour  lines  of  the  sectioned  surface,  the  section  lines  are 
generally  made  at  an  angle  of  45°  with  them. 

The  weight  of  the  section  lines  should  not  exceed  those 
of  the  outline,  they  look  rather  better  if  made  slightly 
lighter.  Considerable  judgment  can  be  displayed  in  the 


WORKING  DRAWINGS. 


81 


adjustment  of  space  and  weight  of  section  lines.  Consult- 
ing practical  drawings  or  the  illustrations  to  this  book  will 
be  helpful.  The  effect  should  never  be  coarse  but  pleas- 
ing, even,  and  not  too  obtrusive. 


Fig.  34  is  an  example  of  sectioned  surfaces.  It  can  be 
seen  that  if  narrow  spaces  are  sectioned  by  relatively 
widely  spaced  lines,  the  effect  is  coarse.  If  on  the  other 
hand,  the  spacing  is  too  narrow  the  effect  will  be  that  of  a 
dark  tone  obscuring  the  outlines  and  any  errors  in  spacing 
are  more  noticeable.  Again,  the  larger  the  surface  to  be 
sectioned  the  wider  can  be  the  spacing  of  the  lines.  Long 
narrow  pieces  should  be  sectioned  by  heavy  lines  closely 
spaced  and  large  areas  by  light  lines  widely  spaced. 

Draftsmen  generally  have  a  maximum  and  minimum 
of  spacing  of  section  lines  that  are  not  very  far  apart, 
nor  do  they  use  many  different  spacings  because  it  is 


82  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 

economical  of  effect  if  sectioning  can  be  made  more  or  less 
mechanical.  One  authority  fittingly  says :  *"When  a  few 
lines  have  been  done  in  section  an  unconscious  rythmic 
action,  as  it  were,  is  established,  just  as  one  beats  time  to 
slow  or  fast  music  without  thinking,  and  the  manipulation 
becomes  mechanical.  *  For  this  reason,'  he  goes  on  to  say, 
4  a  drawing  to  be  inked  should  never  be  sectioned  in  pencil 
first,  otherwise  the  result  is  likely  to  be  as  bad  as  if  one 
were  to  write  his  name  with  a  pencil  and  then  try  to  go 
over  the  lines  with  ink.'  : 

Hence,  it  can  be  seen  that  this  rythmic  action  comes 
more  readily  when  the  eye  is  accustomed  to  a  very  few 
different  sizes. 

Where  more  than  two  surfaces  are  contiguous  to  one 
another  it  is  customary  to  use  30°  or  60°  lines  to  distinguish 
the  third  surface,  but  these  angles  are  not  resorted  to 
unless  it  is  necessary. 

Sometimes  contiguous  surfaces  are  distinguished  from 
one  another  by  having  the  section  lines  fall  uniformly 
short  of  the  limiting  lines  of  the  surface  by  a  small  dis- 
tance, say  A  or  iV  of  an  inch  as  shown  in  Fig.  35.  A 
section  may  be  designated  as  a  longitudinal  or  transverse 
section  according  to  whether  the  plane  of  the  section  is 
parallel  to  the  long  axis  of  the  subject  or  at  right  angles  to 
it. 

If  the  plane  of  a  section  is  horizontal,  it  is  called  a 
sectional  plan,  if  vertical,  a  sectional  elevation,  or  in  other 
directions  it  may  be  called  simply  a  sectional  detail.  If  a 
sectional  plan,  its  place  is  above  or  below  the  elevation, 
according  to  the  angle  used  in  projection  and  it  may  take 

*  C.  W.  McCord,  Mechanical  Drawing,  P.  6. 


WORKING  DRAWINGS. 
FlGUBB    85u. 


83 


the  place  of  a  plan  when  it  is  not*  necessary  to  have  the 
latter  present.  When  it  is,  then  the  sectional  plan  may  be 
placed  either  above  or  below  the  regular  plan  according  to 
the  angle  of  the  projection,  if  there  is  not  convenient  room 
for  this  it  may  be  placed  to  the  right  or  left,  orthogonally 
projected  from  the  plan.  Sometimes,  according  to  cir- 
cumstances, the  section  is  placed  independently  of  the 
regular  projection  views  in  any  convenient  place  on  the 
sheet.  The  importance  of  the  section  view  and  its  value 
in  giving  data  for  construction  determine  the  latter  men- 
tioned choice  of  positions. 

To  designate  a  sectional  plan,  a  broken  line,  for  which 
the  convention  is  variable,  is  drawn  across  the  elevation 
showing  the  position  of  the  theoretical  saw  cut,  and  the 
ends  of  this  line  are  lettered  A— A  or  B— B,  and  so 
referred  to  in  designating  the  sectional  view  (see  Fig.  34). 
The  broken  line  may  consist  simply  of  very  heavy,  short 
lines  just  entering  upon,  and  on  opposite  sides  of,  the 
elevation,  to  call  attention  sharply  to  the  place. 

Sometimes    forms  are   cut    through   which  cannot    be 


84 


NOTES  ON  PRACTICAL  MECHANICAL  DRAWING. 


accurately  represented  by  a  surface  hatched  with  lines;  the 
cross  section  of  an  I  beam  or  a  built  up  girder,  as  in  Fig. 
36.  This  is  difficult  because  the  surfaces  cut  through  are 


FIGURE    No .  86. 


so  narrow  that  it  is  impossible  to  represent  them  to  scale 
by  a  double  line,  in  fact  the  ordinary  line  on  a  drawing 
might  itself  be  far  too  heavy.  Scale  in  thickness  of 
material  then  has  to  be  sacrificed  for  effect  in  showing 
construction. 

Forms  are  not  always  continuously  cut  through.  Only 
a  portion  may  be  sectioned  or  the  plane  of  the  section  may, 
for  convenience  or  economy  of  views,  be  in  reality  two  or 

more  parallel  planes  cutting  through  two  or  more  parts  of 

• 

the  subject;  very  rarely  are  the  planes  made  non-parallel, 
although  such  a  condition  is  not  prohibited  by  any  written 
or  unwritten  laws.  A  very  usual  device  is  to  represent  a 
portion,  say  one-half,  of  an  elevation  as  in  section.  This, 
if  the  subject  be  symmetrical  upon  a  center  line,  will  save 
the  drawing  of  one  view. 

When  the  plane  of  a  section  moves  from  one  place  to 
another,  as  just  explained,  some  conventional  line,  usually 


WORKING  DRAWINGS.  85 

that  for  center  lines,  is  used  to  divide  the  planes  or  the 
sectioned  from  the  non-sectioned  parts.  The  plane  then 
terminated  by  this  limiting  line  has  no  other  limits.  A 
solid  limiting  line  is  not  used  unless  the  material  sectioned 
through  actually  ends  at  this  place,  and  a  new  piece  begins 
beyond  it. 

Where  different  pieces  in  the  same  sectional  plane,  are 
sectioned  in  a  subject,  considerable  taste  can  be  displayed 
in  distinguishing  parts  one  from  another.  Where  the  same 
piece  reappears  as  cut  through  in  the  plane  of  the  section 
it  should  be  treated  by  section  lines  identical  in  weight 
and  spacing  so  as  to  preserve,  in  other  words,  the  con- 
tinuity of  material. 

52.  Standardized  section  lining  has  been  attempted 
with  but  partial  success  by  the  adoption  of  certain  weight 
and  spacing  of  lines  to  be  used  as  representing  different 
materials,  steel,  wrought  iron,  cast  iron,  brass,  etc.  But, 
while  a  well  known  series  has  had  wide  publicity,  that 
approved  by  the  A.  S.  M.  E.,  and  in  use  by  the  Govern- 
ment drafting  offices,  still  its  use  is  not  at  all  universal. 
Each  drafting  office  has  its  own  way  of  treating  sectioning. 

Fig.  37  shows  the  A.  S.  M.  E.  standards,  together 
with  the  spacing  and  weight  of  line  that  are  practical.  Of 
course  these  are  more  or  less  governed  by  the  area  to  be 
treated. 

For  wrought  iron  the  groups  of  lines  should  be 
separated  from  each  other  simply  by  a  little  wider  space 
than  are  the  lines  of  the  group,  the  same  of  steel. 

The  convention  for  glass  is  an  attempt  to  illustrate  the 
play  of  light  one  sees  now  and  then  upon  looking  into  a 


NOTES   ON  PRACTICAL,  MECHANICAL  DRAWING. 

FIGURE    No.    87. 
Cast  Iron.  Wrought  Iron.  Steel. 


Brass. 


Lead,  Babbitt. 


Wood. 


Glass. 


Packing. 


•  .  .  t  . 

//•'•  <'•  -r-V 
'•'//'.•/.•'•'. 

<'.  ''.". 
'  '''-I'". 

'«**.*  ^T*"  *.»'.' 

Brick. 


W^mmm 

W/aw////mm 


room  from  the  outside  through  a  window;  the  several 
masses  of  tinting,  which  by  the  way  should  be  expressed 
by  lines  more  closely  spaced  than  in  sectioning,  are 
irregular  in  their  contour  shape,  yet  grouped  together. 
The  arrangement  of  this  convention  is  after  all  a  matter  of 
taste  of  the  draftsman. 


WORKING  DRAWINGS.  87 

Leather,  sand  or  packing  material  are  expressed  by 
about  the  same  convention.  It  is  made  with  the  writing 
pen;  for  packing,  the  strokes  may  take  the  shape  of 
irregular  lines  like  short  threads. 

In  place  of  a  conventional  section  lining,  materials  may 
be  lettered  W.I.,  C.I.,  S.,  etc.,  on  the  surfaces,  to  show 
what  they  are  made  of,  or  else  a  designating  number  may 
be  used.  The  number  may  lie  between  limits  which,  by 
arbitrary  agreement,  stand  for  a  certain  material;  for 
example,  Nos.  1  to  200  for  cast  iron,  200  to  300  for  wrought 
iron,  etc. 

* 

53.     Some  practical  points  about  sectioning. 

Sectioned  views  are  not  used  in  working  drawings  unless 
it  cannot  be  avoided  or  unless  their  use  is  economical  of 
views,  and  consequently  of  tune,  and  when  not  sacrificing 
clearness.  They  are  used  less  as  a  vehicle  for  dimensions, 
also,  than  they  are  to  show  form,  what  is  solid  and  what  is 
hollow,  what  is  continuous  in  the  various  materials.  They 
are  not  desirable  as  a  vehicle  for  dimensions  because  of 
the  interference  of  the  section  lines  with  the  dimension 
lines  and  figures.  When  dimensions  have  to  be  put  across 
a  dimensioned  surface,  space  is  left  at  least  for  the  figures, 
sometimes  for  the  dimension  lines  and  the  arrow  heads. 
Aside  from  legibility,  the  presence  of  a  dimension  should 
be  at  once  apparent  through  its  prominence  on  the  drawing. 

A  sectioned  view  should  always  show  in  full  line  that 
which  lies  within  the  plane  of  the  section,  all  that  is 
beyond  this  should  also  be  shown  in  full  line  which  is  not 
covered  by  the  surface  sectioned.  If  it  is  desirable  to 
show  what  is  covered,  it  should  be  dotted  as  in  any  other 


88  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 

hidden  construction.  Of  course  nothing  should  be  shown 
of  that  part  supposed  to  have  been  removed  when  the 
subject  was  cut  through. 

Section  lining  should  be  done  directly  in  that  medium 
in  which  the  drawing  is  to  be  left,  and  the  spacing  calcu- 
lated with  the  unaided  eye.  To  do  this  well  will  require  a 
little  practice;  a  few  hints  which  follow  may  be  found 
helpful :- 

Sketch  the  sectioned  surfaces  roughly  free-hand 
in  pencil  to  show  which  are  sectioned  surfaces  and 
which  are  not,  and  to  show  what  direction  of 
section  lines  to  use. 

Hold  an  arm  of  the  triangle,  when  possible,  one 
edge  of  which  is  guiding  the  section  lines,  by  the 
thumb  and  first  or  second  fingers  so  that  the 
triangle  may  be  made  to  creep  along  the  paper. 

Use  the  edge  of  the  triangle  only  for  an  approx- 
imate adjustment  of  spacing,  let  the  pen  point  give 
it  more  accurately. 

Mechanical  devices  called  section  liners  have  been 
invented  for  spacing  lines  evenly  but  they  are  not  in 
general  use  by  draftsmen.  They  fail  because  the  pen 
cannot  be  held  so  invariably  the  same  way  with  respect  to 
the  ruling  edge  that  the  section  liner  can  be  depended 
upon  to  space  automatically. 

If  a  surface  to  be  sectioned  is  broken  up  so  that  the 
lines  in  all  places  cannot  be  drawn  continuously  across  it, 
as  in  a  transverse  section  of  a  hollow  cylinder,  a  line  may 
be  followed  along  from  its  beginning  to  its  end  across  the 
subject  before  going  on  with  the  next  one,  or,  a  method  to 


WORKING  DRAWINGS. 

be  prefered  is  to  draw  a  group  of  lines  in  one  place  and 
afterwards  in  another  on  the  opposite  side. 

In  the  section  view  of  features  which  wrap  around  one 
another  like  a  valve  with  its  stem,  gland  and  body,  it  is 
desirable  to  begin  with  the  innermost  parts  and  develop 
outward  from  them. 

Sometimes  labor  is  saved,  in  hurried  work,  by  not 
section  lining  entirely  across  relatively  large  surfaces  but 
by  sectioning  only  around  the  edges,  stopping  the  section 
lines  along  imaginary  lines  parallel  to  the  edges  success- 
ively of  the  surface  to  be  sectioned. 

Long  members  of  uniform  cross  section  like  I  beams, 
etc.,  sometimes  cannot  be  shown  their  true  length  in 
a  drawing  without  reducing  too  much  their  transverse 
dimension.  To  overcome  this  they  are  assumed  to  be 
broken  as  shown  in  Fig.  38.  The  over-all  dimension  is 


FIQUBE   No.   88. 


given  and,  to  save  a  separate  view,  the  exact  shape  of  the 
cross  section  may  be  shown  on  one  of  the  pieces,  as  if  the 
plane  of  the  section  were  turned  through  an  angle  of  90°. 

54.  The  rules  of  orthographic  projection  are  violated  in 
sections,  things  are  done  which  are  not  strictly  protective 
or  follow  the  theoretical  saw  cut.  This  is  because  clear- 
ness of  construction  is  paramount. 


90  NOTES   ON   PRACTICAL  MECHANICAL  DRAWING. 

For  example,  it  is  of  no  use  to  section  longitudinally 
through  a  bolt  or  nut,  the  identity  is  not  as  readily 
distinguished.  Bolts,  washers,  shafts,  rods,  or  other  solid 
pieces,  having  a  relatively  long  axis  proportional  to  their 
diameter,  are  never  sectioned  longitudinally. 

The  spoke  of  a  ivlieel  is  not  cut  through  longitudinally, 
if  it  should  happen  to  come  within  the  plane  of  a 
section.  The  rim  and  hub  are  the  important  features,  the 
spoke  is  but  a  relatively  narrow  connecting  link  between 
the  two.  If  sectioned,  it  is  apt  to  give  the  impression  of  a 
wheel  with  a  web  or  diaphragm  connecting  rim  and  hub. 

It  may  be  set  down,  as  a  general  rule,  that  a  rib,  an 
arm  of  a  pulley,  or  any  comparatively  thin  piece  should 
not  be  sectioned  by  a  cutting  plane  which  is  parallel  to  its 
longest  bounding  surfaces. 

The  surface  of  a  cut  is  not  interrupted  merely  for  the 
sake  of  showing  a  fastening  or  other  minor  feature.  For 
example,  if  sectioning  longitudinally  through  a  cylinder 
and  its  head,  and  if  the  bolts  fastening  body  and  head 
should,  some  of  them,  happen  to  come  within  the  plane  of 
the  section,  they  would  not  be  sectioned,  but  either 
omitted  or  shown  in  dotted  where  they  passed  through  the 
sectioned  material  and  in  full  line  elsewhere. 

On  the  other  hand,  if  we  have  a  sectioned  side  view  of 
any  thing,  having  radially  placed  holes,  and  the  plane  of 
the  section  does  not  pass  through  one  or  more  of  them,  nor 
is  their  arrangement  clearly  shown  in  another  view,  one 
hole  should  be  cut  through,  and  at  its  true  radial  distance 
from  the  center,  to  furnish  information  lacking  elsewhere. 

A  key -way  in  a  collar  should  not  be  sectioned  longi- 
tudinally with  the  collar,  but  should  be  shown  with  a 
dotted  line. 


WORKING  DRAWINGS.  91 

It  is  hardly  worth  while  to  multiply  instances  of  viola- 
tion of  projection  in  sections;  new  cases  are  likely  to  arise 
continuously.  Suffice  it  that  features  are  not  shown  in 
section  where  no  information  would  be  gained  thereby,  no 
matter  whether  they  come  within  the  plane  of  the  saw  cut 
or  not. 

Sectional  details  are  placed  either  near  the  part  to 
which  they  are  related  or  grouped  together  in  any  conve- 
nient place  on  the  drawing,  there  is  no  rule  governing.  If 
placed  near  the  principal  form  they  are  generally  made 
protective  with  it,  except  that  the  sectional  projection  may 
be  made  on  a  supplementary  plane  not  corresponding  to 
the  co-ordinate  planes. 

55.     Dimensioning: 

Dimensions  are  a  most  important  part  of  a  working 
drawing.  If  the  scale  on  the  drawing  and  the  dimensions 
do  not  agree,  the  latter  are  assumed  to  be  correct  and 
govern  the  men  in  the  shop.  All  that  the  workman  needs 
to  know  must  be  put  thereon,  either  in  dimensions  or 
footnotes,  the  latter  being  equally  as  important  as  the 
dimensions. 

Sizes  from  a  machine  should  always  be  taken  with  the 
foot  rule  and  calipers,  not  with  the  scale.  The  rule  should 
be  put  as  close  to  the  distance  to  be  measured  as  possible ; 
for  accurate  work,  use  the  machinists'  dividers,  and  apply 
them  afterwards  to  the  foot  rule. 

The  machinists'  dividers  are  used  to  ascertain  sizes  of 
flat  surfaces,  the  calipers,  inside  and  outside,  are  used  to 
get  the  diameters  of  holes  and  cylindrical  forms.  After  a 
diameter  has  been  obtained  with  the  inside  calipers,  one 


92  NOTES  ON  PRACTICAL,  MECHANICAL  DRAWING. 

end  should  be  set  flush  with  the  end  of  the  foot  rule.  If 
convenient,  place  both  against  a  flat  surface.  With  the 
outside  calipers,  rest  one  of  the  arms  against  one  of  the 
end  faces  of  the  rule.  These  directions  will  facilitate  the 
making  of  rapid  measurements. 

A  knowledge  of  processes  of  manufacture  will  show 
that  it  is  a  waste  of  effort  to  measure  everything  to  the 
thousandths  of  an  inch,  as  some  tight  fits,  of  course,  have 
to  be.  Rough  castings  cannot  be  measured  to  a  sixteenth 
of  an  inch  with  accuracy.  Work  that  is  to  be  machined 
may  or  may  not  require  to  be  very  accurate.  A  tight  fit 
may  call  for  accuracy  to  a  thousandth  of  an  inch,  another 
kind  to  a  hundredth.  Discrimination  should  be  used  in 
dimensioning.  As  an  illustration  of  the  application  of 
approximate  and  exact  measurements,  take  a  line  of 
sub-divided  dimensions,  which  lie,  on  the  one  hand, 
between  a  finished  surface,  and  the  other  the  end  of  a 
casting.  The  last  sub-divided  dimension  at  the  casting 
end  should  be  omitted,  and  in  its  place  an  overall  dimen- 
sion should  be  given.  The  man  who  makes  the  casting 
will  get  the  measurements  he  needs,  while  he  who  does 
the  machine  work  and  finishing  will  get  those  exact  sizes 
he  wants,  and  neither  will,  in  any  way,  hamper  the  other. 

All  dimensions  should  be  final  working  ones,  no 
allowance  should  be  made  for  shrinkage  of  castings,  etc. 

The  distance  between  chief  centers,  and  if  the  subject 
is  symmetrical  upon  a  center  line,  the  distances  also  of 
these  centers  from  the  center  line  is  always  necessary. 

The  overall  dimensions  are  needed  in  every  case.  The 
subdivided  ones  between  depend  upon  the  nature  of  the 
work  which  is  to  be  done  upon  the  particular  piece,  all  the 


WORKING  DRAWINGS.  93 

subdivisions  may  or  may  not  be  needed,  they  should  be 
shown  continuously  on  a  line.  It  frequently  happens  that 
there  are  two  or  three  main  subdivisions,  like  the  distances 
of  the  sides  or  ends  of  a  piece  from  one  or  two  important 
center  lines,  and  in  addition  the  distances  of  other  smaller 
parts  from  these  center  lines.  Where  such  exist  we  have 
three  classes  of  dimensions.  They  ought  generally  to  be 
figured  up  complete  in  each  case  to  the  overall,  if  for  no 
other  reason  than  that  each  may  be  a  check  upon  the 
other.  Aside  from  this,  they  may  be  needed  in  construct- 
ing the  piece.  The  three  sets  should  be  close  to  one 
another,  the  overall  the  outermost,  and  the  subdivided  the 
innermost  of  the  three.  The  relation  between  the  three 
should  be  at  once  apparent. 

The  dimensions  should  be  put  on  a  design  about  as  fast 
as  the  forms  are  constructed,  because  at  any  time  a 
preceding  dimension  may  be  needed  to  find  a  subsequent 
one.  And,  furthermore,  it  is  a  check  on  what  is  needed 
for  construction. 

If  the  drawing  is  made  from  a  model,  as  for  study 
purposes,  it  is  best  to  leave  the  dimensions  until  the  last, 
as  one  thing  to  consider  at  a  time  leads  to  accuracy. 

In  constructing  a  drawing,  and  in  setting  off  measure- 
ments and  subdividing  distances,  use  the  scale  where 
possible.  Use  the  dividers  or  compasses  only  where  it  is 
unavoidable. 

If  the  drawing  is  made  from  a  model  and  the  dimension- 
ing left  for  the  last,  then  the  following  system  should 
prevail : 

(a.)     Start  at  the  top  of   the  original,   and 

going  down,  note  all  those  things  requiring  hori- 


94  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 

zontal  dimensions,  and  put  the  same  on  the  views 

which    will  need  them,   or    show  them    to    best 

advantage. 

(&.)    Starting    at   the    left,    and    proceeding 

toward  the  right,  move   similarly,  recording  the 

vertical  dimensions. 

(c.)     Locate  all  radii,  diameters  and  oblique 

dimensions. 

(d.)    Check  everything. 

These  steps  may  again  be  subdivided  into  more. 
After  locating  some  thing  requiring  a  dimension,  mark 
simply  the  place  where  it  is  to  go  on  the  drawing,  by  either 
sketching  in  the  dimension  lines  and  arrow  heads  free 
hand,  or  with  the  rule.  After  the  place  and  the  full 
number  of  all  dimensions  are  located,  then  the  foot  rule 
should  be  applied,  and  the  value  of  the  several  dimensions 
ascertained  and  recorded. 

In  inking  the  dimensions  on  a  drawing  made  from  the 
model,  the  same  procedure  should  be  gone  through  with 
except  that  the  arrow  heads  should  be  put  in  first,  and  the 
dimension  figures  next.  Nothing  in  the  way  of  precaution, 
to  preserve  accuracy  in  dimensioning  can  be  out  of  place. 
The  inking  of  the  limiting  lines  for  dimension  lines  should 
precede  the  dimension  lines  themselves,  for  the  same  reason 
that  the  arrow  heads  should  precede  the  figures.  For,  if  the 
former  are  not  done  first,  they  are  apt  to  be  overlooked. 

The  practice  is  common  in  the  better  drafting  rooms  to 
give  accurate  dimensions  w  decimals  and  approximate  in 
fractions.  Structural  steel  drawings  are  dimensioned  in 
decimals.  When  the  dimensions  are  given  in  decimals, 
the  inch  or  foot  marks  should  be  placed  in  front  of  the 


WORKING  DRAWINGS.  95 

decimal  to  replace  the  whole  number.  Similarly,  in  case 
of  dimensioning  in  feet  and  inches,  and  the  inches  are 
zero,  or  less  than  one,  a  zero  mark  with  the  inch  sign  over 
hVshould  always  be  put  in  the  inches7  place,  or  a  zero  in 
front  of  the  fraction. 

Dimension  lines  are  usually  not  made  of  any  particular 
convention  of  line,  because  they  are  so  varied  in  length. 
Generally,  they  are  composed  of  several  dashes  when 
long,  varying  in  length  according  to  the  distance  to  be 
dimensioned.  Some  drafting  rooms  use  a  solid  line,  but 
much  lighter  than  any  of  the  other  lines  of  the  drawing, 
and  in  rendering  in  ink  where  blue  prints  are  to  be  made 
from  it,  they  are  made  in  red  ink  with  a  little  black  mixed 
with  it  to  render  it  opaque,  and  make  it  show  on  the  blue 
print  as  a  very  light  blue  line. 

Dimensions  should  not  be  crowded  between  limits  too 
narrow  to  receive  them.  The  several  ways  of  specifying 
linear  dimensions,  diameters  and  radii  are  shown  in 
Fig.  39. 

When  a  dimension  is  placed  outside  a  form,  limiting 
lines  must  be  run  to  the  form  and  perpendicular  to  the 
direction  of  the  distance  which  is  to  be  specified.  They 
should  be  continuous  lines,  running  just  a  trifle  beyond 
the  dimension  line,  and  to  a  point  just  a  trifle  short  of  the 
outlines  of  the  subject,  as  shown  in  the  Fig.  39.  The  foot 
and  inch  marks  may  be  as  shown,  either  way,  but  the 
upper  of  the  two  is  the  best  because  there  can  be  no 
misunderstanding  of  the  symbol.  The  dash  should  always 
be  put  between  the  foot  and  inch  figures,  to  prevent 
misunderstanding. 

The  dash  marks  when  used  for  the  feet  and  inches 
should  be  distinct,  and  easily  distinguished  from  acci- 


NOTES   ON   PRACTICAL  MECHANICAL  DRAWING. 

FlGUKE    NO.    39. 
// 

*-  3 

Jit 


~ 
2-6 


dental  marks.  They  should  go  above  and  to  the  right  of 
the  figures,  be  about  one-half  the  height  of  the  figures,  thick 
at  the  top  and  pointed  at  the  bottom  as  the  writing  pen 
would  naturally  make  them  with  the  spreading  of  the  nibs 
at  the  beginning  of  the  stroke. 

The  arrow  heads  at  the  ends  of  dimension  lines  should 
be  made  with  the  writing  pen,  sharp  and  concave  with  the 
sides  of  the  arrow  at  about  an  angle  of  30°  to  one  another. 
Care  should  be  exercised  to  bring  the  point  of  the  arrow  to 
exactly  the  limit  it  is  to  accentuate. 

Where  leaders  are  taken  from  a  point  to  a  dimension, 
the  line  can  either  be  ruled  or  made  free-hand.  The 
neatest  appearance  is  attained  when  it  is  ruled. 

The  figures  of  a  dimension  should  be  printed,  not 
written  hurriedly.  Figures  that  are  from  one  to  one  and 
one-half  times  as  wide  as  they  are  high  are  the  best. 
Where  fractions  occur,  the  fraction  line  should  be  perpen- 
dicular to  the  line  connecting  the  two  figures,  or  in  other 


WORKING  DRAWINGS.  97 

words,  horizontal  when  normally  reading  the  figures. 
Recent  practice  puts  the  numerator  exactly  above  the 
denominator  and  omits  the  fraction  line. 

The  fraction  figures  may  be  made  as  large  as  those  of 
the  whole  number,  but  also  can  equally  appropriately  be 
made  slightly  less.  A  good  working  rule  is  to  make  them 
just  a  trifle  smaller  than  the  whole  numbers. 

Notes,  should  be  made  concerning  materials  or  finish, 
written  on  the  drawing  in  off-hand  lettering  or  they  may 
be  included  in  the  bill  of  materials.  If  the  latter,  the  note 
will  state  the  material  used,  how  each  part  is  to  be 
finished,  and  the  number  of  pieces  required.  Special 
directions  pertaining  to  making,  painting,  shipping,  etc., 
may  even  be  given  in  notes;  also  sometimes,  notes 
pertaining  to  erection  are  added,  like  " These  rivets  are  to 
be  field  driven." 

To  summarize  briefly:  — 

Those  dimensions  should  be  put  on  which  are  needed 
in  the  various  processes  through  which  pieces  are  to  be 
put  in  making,  should  be  clear  and  not  crowded,  and 
should  furthermore:— 

Read  from  the  bottom  and  right  hand  sides. 

Arrow  heads  should  be  small,  neat,  sharp  pointed, 
clear  and  with  small  angle  between  the  sides. 

No  dimensions  should  be  put  on  center  lines. 

No  lines  should  be  drawn  through  dimensions. 

All  dimension  figures  should  be  of  the  same  size. 

Dimension  figures  should  be  in  the  center  of  the 
dimension  line,  where  possible. 

All  figures  should  be  of  the  same  size. 

All  measurements,  in  general,  should  be  made  from 
center  lines  or  from  finished  surfaces. 


98  NOTES   ON   PRACTICAL  MECHANICAL  DRAWING. 

In  cross  sections,  leave  a  clear  space  unsectioned 

for  the  dimensions. 
The  most  appropriate  dimensions   should    be  on 

each  view. 

Similar  parts  should  be  dimensioned  in  like  places. 
Dimensions  should  not,  in  general,  be  repeated. 

Dimensioning  of  certain  features :  — 

A  tapped  hole  is  one  bored  to  receive  a  screw  and  is 
dimensioned  for  the  required  diameter  of  bolt  or  screw,  as 
for  a  1J"  screw.  If  cast,  the  hole  is  specified  as  cored  for 
a  sufficiently  smaller  size  to  permit  of  its  being  tapped  out 
to  the  required  size.  If  a  hole  is  tapped  for  a  bolt,  the 
drawing  may  or  may  not  show  two  concentric  circles  to 
stand  for  the  base  and  the  crown  of  the  thread.  If  only 
one  is  shown,  it  will  be  the  circle  which  specifies  the  diam- 
eter of  the  screw,  namely,  the  crown  of  the  screw  thread. 

Bolts  for  a  tapped  hole  will,  if  standard,  only  require 
the  size  or  diameter  which  may  be  specified  as  a  dimen- 
sion, or  by  a  note  to  one  side,  the  length  under  the  head 
and  the  length  that  is  threaded,  the  latter  specified  gen- 
erally as  a  distance  from  the  end  of  the  bolt.  If  the  bolt 
is  not  standard,  it  will  require,  in  addition  to  the  above 
dimensions,  the  height  and  diameter  of  the  head  and 
number  of  threads  per  inch.  If  the  end  of  a  screw  is 
rounded,  the  dimensions  of  the  overall  and  the  length  that 
is  threaded  should  be  given  to  the  corner  and  not  to  the 
extreme  end. 

When  bolt  holes  are  spaced  equally  around  a  center 
upon  a  disc  or  a  cylinder  head,  for  example,  a  circle  pass- 
ing through  all  their  centers,  together  with  radial  lines, 


WORKING  DRAWINGS. 

also  passing  through  the  centers,  constitute  center  lines 
for  these  forms,  and  the  radius  of  this  bolt  circle  is  given, 
and  also  the  number  of  the  bolts,  or  the  angular  distance 
between  them. 

Angles,  if  specified,  may  be  given  in  degrees,  or  by 
co-ordinates  or  by  tangents,  depending  upon  circum- 
stances. If  in  degrees,  an  arc  is  struck  from  the  vertex  of 
the  angle  as  center,  the  dimension  liie  constituting  this 
arc;  if  by  co-ordinates,  any  two  distances  at  right  angles 
to  each  other  are  used,  measuring  from  each  other  and  the 
vertex  of  the  angle ;  if  by  tangents,  it  is  the  length  of  a 
perpendicular  measured  from  a  base,  which  is  one  side  of 
the  angle,  of  length  one,  measuring  from  the  vertex  of  the 
angle.  Measurement  by  co-ordinates  is  of  particular  use 
to  the  pattern  maker. 

Always  dimension  filleted  or  rounded  corners,  where  an 
adjoining  finished  surface  does  not  prevent  and  give  the 
radius  of  the  fillet,  as  its  size  may  be  important  in  adding 
strength  to  the  angle. 

The  dimensions  concerning  a  number  of  rivets  or  small 
bolt  holes  in  a  right  line,  should  be  written  between  the 
arrowheads  of  an  overall.  It  should  contain  the  number, 
size,  distance  apart,  as  well  as  the  distance  of  centers 
overall.  The  distance  of  the  end  holes  to  the  end  of  the 
piece  should  regularly  be  given. 

Wliere  a  taper  is  required,  it  should  be  dimensioned 
with  the  taper  per  foot  of  length.  Occasionally,  it  is 
specified  by  giving  the  dimension  at  each  end  of  the  taper; 
where  this  is  done  the  approximate  taper  ought  also  to  be 
given. 

Tine  dimensions  of  boards  and  iron  plates  should  be 


100  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 

specified  in  the  order  of  width,  thickness  and  length,  for 
example  a  board  14"xi''x8'  — 0".  The  grain  will  be 
parallel  to  the  8'  —  0"  edge. 

56.  Notes   for  kind  of   finish    are    required    on    some 
drawings,  as  file  finish,  grind  finish,  etc. 

For  plane  finish,  an  f  is  put  across  the  edge  view  of 
the  surface  to  be  so  treated.  A  note  may  be  added,  when 
the  finish  is  to  be  of  a  different  kind.  It  is  necessary  to 
designate  it  so  that  extra  material  may  be  allowed  in  the 
casting. 

A  few  of  the  kinds  of  finish  are  as  follows:  — 
Polish:— Smooth  and  glossy  surface  without  accu- 
rate adherence  to  dimensions. 
Finish  and  polish:  —  Smooth  and  glossy  surface 

without  sacrifice  of  accuracy  of  work. 
Spot  face:— Making  the  spot  true. 
Finish  and  scrape:— Shape  to  dimensions  by  cut- 
ting tool  and  afterwards  scrape  the  surface. 
Finish  and  grind:— Shape  to  dimensions  with  cut- 
ting tool  and  grind. 

Trim:  —  Shaping  by  any  convenient  means   as 
chipping,  filing,  grinding,  etc. 

57.  Drawings  are   marked   with  symbols   in  the  lower 
right  hand  corner  and  also  in  the  upper  left  hand  corner, 
upside  down,  so  as  to  be  read  whichever  way  the  drawing 
happens  to  lie.    The  character  of  the  mark  depends  upon 
the  system  of  filing  used.    In  some  cases,  a  certain  class 
of  machines  has  numbers  between  certain  limits  and  a 
letter  arbitrarily    designates    the   size    of    the  sheet,    as 
D-188, 


WORKING  DRAWINGS.  101 

58.    The  checking  of  drawings   should    be    done   by 
methodical  steps;   a  bird's  eye  view   is  not  a  sufficient 
check.    The  drawing  should  be  checked  through  approxi- 
mately the  duplicate  of  steps  by  which  it  was  originally 
made,  and  each  step  should  be  carried  carefully  through- 
out before  the  next  step  is  undertaken,  as  follows:  — 
(1.)     Identify  every  piece  of  a  subject  to  see  if  all 
are  fully  shown,  and  also  the  requisite  views  of 
each. 
(2.)    Note  lines  of  various  views  for  completeness 

and  correctness. 
(3.)     See  that  all  dimensions  are  given  that  are 

needed,  also  working  notes. 

(4.)  Scale  every  dimension  to  see  if  it  is  cor- 
rect, putting  a  check  mark  alongside  of  each 
as  checked. 

(5. )     See  if  they  correspond  with  each  other  in  dif- 
ferent parts,  in  the  assembly  and  the  details. 
(6.)     See  if  arrow  heads  are  all  shown. 
(7.)     See  if  dimensions  are  well  placed. 
(8.)     See  if  accents  for  feet  and  inches  are  all  cor- 
rect, and  fractions  or  decimals  plain. 
(9.)     See  if  center  lines  are  all  in  and  correctly 

shown. 

(10.)  Finally  check  for  supplementary  notes  and 
directions,  including  bill  of  materials,  if  there 
is  any. 

Checking  is  often  done  by  other  than  the  draftsman. 
The  final  checker,  perhaps,  may  be  a  man  who  does 
nothing  else,  and  who  is  held  responsible  for  the  results 
after  the  drawing  leaves  the  drafting  room. 


102 


NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 


5Q.     Conventions  in  common  use  on  working  drawings: — 

There  are  a  number  of  conventional  methods  of 
representing  forms  and  certain  constructions,  which  recur 
very  frequently  in  working  drawings. 

Different  establishments  have  their  particular  con- 
ventions, used  in  diagraming,  etc.,  among  these  conven- 
tions, a  characteristic  group  is  those  used  in  electrical 
work.  Fig.  40  shows  a  few  of  these. 

FIGURE    No.    40. 


MOTOR         ALTERNATOR    VOLTMETER  AMMETER     STORAGE  BATTERY 

.    a 

<p<]xp(p(p({)       XXXX  -AAA- 

*        *  ON  OFF 

PRIMARY  BATTERY  BELL  INCANDESCENT  CIRCUIT   ARC  LAMPS  RESISTANCE 


VARIABLE  RESISTANCE  SWITCH  TRI-PHASE  [STARty TRIANGULAR  CONNECTIONS] 


RHEOSTAT     JOINED  WIRES    CROSSED  WIRES     CONDENSER- 

When  a  long  thin  member  like  an  angle,  or  T  bar,  or  I 
fiar,  etc.,  is  broken  for  any  reason,  the  approximate  shape 
of  the  section  is  shown  on  the  end.  Sometimes  the 


WORKING  DRAWINGS. 


103 


accurate  shape  is  given  so  that  one  view  may  do  for  two. 
See  Fig.  41. 

FIGUBE    NO.    41. 


1 

1/////S 

A  round  shaft  or  rod  is  broken,  as  shown,  and  if 
hollow,  the  approximate  thickness  of  the  metal  is  indi- 
cated. The  curve  of  the  break  may  be  put  in  with  the 
curved  rule,  but  also  may  be  done  free-hand.  Wood  is 
shown  by  representing  the  splintering  that  is  apt  to 
accompany  a  break. 

Now  and  then  colors  in  very  pale  tints  are  used  to 
represent  various  materials  of  construction.  They  ought 
only  to  be  put  on  drawings  which  are  stretched  to  the 
board.  The  following  are  the  most  important  of  these: 

Cast  iron,  payne's  grey. 

Wrought  iron,  Prussian  blue. 

Steel,  Prussian  blue  with  tinge  of  carmine. 

Brass  outside,  gamboge. 

Brass  in  section,  carmine. 

Grained  or  knotted  wood,  burnt  sienna. 

Earth,  burnt  umber. 

Brick,  light  or  Venetian  red. 

Masonry,  wash  of  india  ink  with  tinge  of  blue. 


104  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 

More  natural  effect  can  be  given  to  other  materials 
like  wood,  water,  etc.,  according  to  the  artistic  skill  of  the 
draftsman. 

In  some  elaborate  drawings,  a  nice  effect  is  obtained 
by  shading,  where  possible,  with  the  india  ink  lines  and 
putting  a  tint  over  these  of  the  convention  for  the  material 
shown. 

Since  the  ability  to  put  on  a  good  flat  tint  is  a  neces- 
sary accomplishment  of  the  civil  engineer,  the  following 
extracts  upon  the  subject  are  quoted  from  F.  N.  Willson's 
"Theoretrical  and  Practical  Graphics." 

4 'The  surface  to  be  tinted  should  not  be  abraded  by 
sponge,  knife  or  rubber." 

44  The  liquid  employed  for  tinting  must  be  free  from 
sediment,  or  if  the  latter  is  present,  it  must  be  allowed  to 
settle  and  the  brush  dipped  only  in  the  clear  portion  at 
the  top.  Tints  may,  therefore,  best  be  mixed  in  an  artist's 
water-glass,  rather  than  in  a  shallow  receptacle. "- 

4 'Tints  are  best  prepared  from  the  india  ink  in  cakes, 
and  from  other  water  colors  in  the  pans.  The  size  of  the 
brush  should  bear  some  relation  to  that  of  the  surface  to 
be  tinted." 

4 'Since  tinting  and  shading  can  be  successfully  done, 
after  a  little  practice,  with  only  penciled  limits,  there  is 
but  little  excuse  for  inking  the  boundaries ;  but  if  for  the 
sake  of  definiteness,  the  outlines  are  inked  at  all,  it  should 
be  before  the  tinting,  and  in  the  finest  of  lines,  preferably 
of  4 water  proof  ink,'  although  any  ink  will  do,  provided  a 
soft  sponge  and  plenty  of  clean  water  are  applied  to  remove 
any  excess  that  will  4run.'  The  sponge  is  also  to  be  the 
main  reliance  of  the  draftsman,  for  the  correction  of  errors 


WORKING  DRAWINGS.  105 

in  brush  work;  the  water,  however,  and  not  the  friction, 
to  be  the  active  agent.  An  entire  tint  may  be  removed  in 
this  way  if  it  seems  desirable." 

"When  beginning  work  incline  the  board  at  a  small 
angle,  so  that  the  tint  will  flow  down  after  the  brush..  For 
a  flat  tint,  start  at  the  upper  outline  of  the  surface  to  be 
covered,  and,  with  the  brush  full,  yet  not  so  as  to  prevent 
its  coming  to  a  good  point,  pass  lightly  along  from  left  to 
right,  and  on  the  return  carry  the  tint  down  a  little  further, 
making  short,  quick  strokes,  with  the  brush  held  almost 
perpendicularly  to  the  paper.  Advance  the  tint  as  evenly 
as  possible  along  a  horizontal  line;  work  quickly  between 
outlines,  but  more  slowly  along  outlines,  as  one  should 
never  overrun  the  latter,  and  then  resort  to  'trimming'  to 
conceal  lack  of  skill.  It  is  possible  for  any  one,  with  care 
and  practice,  to  tint  to,  yet  not  over,  boundaries." 

44  The  advancing  edge  of  the  tint  must  not  be  allowed 
to  dry  until  the  lower  boundary  is  reached." 

<4No  portion  of  the  paper,  however  small,  should  be 
missed  as  the  tint  advances,  as  the  work  is  likely  to  be 
spoiled  by  retouching." 

"Should  any  excess  of  tint  be  found  along  the  lower 
edge  of  the  figure,  it  should  be  absorbed  by  the  brush, 
after  first  removing  the  latter's  surplus  by  means  of 
blotting  paper." 

44  To  get  a  dark  effect,  several  medium  tints  laid  on  in 
succession,  each  one  drying  before  the  next  is  applied, 
give  better  results  than  one  dark  one." 

44 A  tint  will  spread  much  more  evenly  on  a  large 
surface,  if  the  paper  is  slightly  dampened  with  clean 
water.  As  the  tint  will  follow  the  water,  the  latter  should 


106  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 

be  limited  exactly  to  the  intended  outlines  of  the    final 
tint." 

60.  Tracings: 

Usually  blue  prints  are  made  from  drawings  to  use  in 
shops,  etc.  Tracings,  or  tracing  cloth  are  the  best  for  this 
purpose.  The  drawings  may  either  be  made  on  manila  or 
detail  paper,  as  it  is  called,  or  they  may  be  made  directly 
upon  the  rough  side  of  the  tracing  cloth. 

A  few  directions  are  necessary  upon  the  handling  of 
the  tracing  cloth.  The  penciling,  as  well  as  ordinary  dirt 
and  soil,  can  be  cleaned  off  by  rubbing  with  gasoline, 
ether,  benzine,  or  any  highly  volatile  substance.  Before 
inking  on  the  cloth,  a  little  chalk  should  be  rubbed  over 
the  surface  with  a  rag,  for  there  is  more  or  less  grease  apt 
to  be  present,  and  it  interferes  with  the  drawing  of  lines  in 
ink.  If  the  fibres  should  get  at  all  torn  or  injured,  they 
may  be  repaired,  partly,  by  rubbing  with  soapstone  or 
hard  beeswax.  The  soapstone  comes  convenient  in  the 
form  of  the  soapstone  pencil. 

Special  care  is  necessary  in  inking  on  cloth,  particu- 
larly if  the  smooth  side  is  used.  The  lines  made  by  the 
pen  are  apt  to  be  thicker  by  spreading,  and  consequently 
blots  are  easy  to  make.  The  precautions  to  be  observed 
are  to  carry  less  ink  in  the  pen,  than  if  working  on  paper r 
and  to  be  sure  that  lines  are  dry  before  working  up  against 
them.  Speed  in  crossing  a  line,  or  working  from  and  to 
lines,  is  necessary.  Mistakes  are  not  so  easy  to  correct. 

61.  The  V  and  square  threaded  screws  are  based  upon 
the  curve  know  as  a  helix.     If  a  point  moves  around  the 
surface  of  a  circular  cylinder  at  a  uniform  rate,  and  at  the 


WORKING  DRAWINGS.  107 

same  time  moves  at  a  uniform  rate  in  the  direction  of  the 
axis  of  the  cylinder,  it  will  generate  the  helix.  From 
co-ordinate  geometry,  a  curve  plotted  between  co-ordinates 
which  have  a  directly  proportional  relation  to  one  another, 
will  be  a  straight  line.  Hence,  the  helix  may  be  defined 
as  the  shortest  line  which  can  be  drawn  upon  a  circular 
cylinder  between  two  points  that  lie  neither  upon  the  same 
right  section  or  upon  the  same  right  line  element. 

62.  To  study  the  helix  in  projection,  draw  a  cylinder  in 
the  third  angle  (as  Fig.  42)  with  axis  parallel  to  the  vertical 
plane.  Assume  a  point  to  be  at .  0,  and  to  move  around 
the  cylinder  in  the  direction  of  the  arrow  through  equal 
distances,  1,2,  3,  etc.  Let  it  move  also  up  the  cylinder 
through  any  given  distance,  until,  after  it  has  completed 
one  revolution  of  the  cylinder,  it  reaches  a  position,  p' , 
directly  above  0' .  The  distance,  o'p' ,  is  known  as  the 
pitch  of  the  curve.  As  both  motions  are  uniform,  the 
point  will  travel  to  1,  which  is  one-twelfth  of  the  circum- 
ferential distance  in  the  same  time  that  it  travels  one- 
twelfth  of  the  distance  of  o'p'  towards  p' ,  and  to  2,  which 
is  one-sixth  of  the  circumferential  length,  as  it  goes  one- 
sixth  of  the  distance,  o'p' ,  towards  p'  and  so  on.  Hence, 
to  plot  the  curve,  divide  the  circumference  of  the  plan  into 
any  convenient  number  of  equal  parts,  and  the  pitch  into 
the  same  number  of  equal  parts.  By  noting  the  points  of 
intersection  of  the  perpendiculars  to  the  ground  line, 
through  the  divisions  of  the  circumference  and  parallels  to 
the  ground  line,  through  the  corresponding  divisions  of  the 
pitch,  points  of  the  curve  may  be  found. 


108  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 

FIGURE  No.   42. 


WORKING  DRAWINGS.  109 

63.  Certain   peculiarities   of   the   curve   deserve    notice: 

(a.)  It  is  tangent  to  the  contour  elements  of  the  cylinder 
at  points,  o'  and  6.  (6.)  It  changes  curvature  at  point, 
3,  midway  of  the  contour  elements,  The  tangent  to  the 
curve  at  3  shows  the  angular  pitch,  which  is  the  ratio  of 
the  linear  pitch  to  the  circumferential  distance,  (c.)  The 
curve  is  sharpest  at  o'  and  gradually  grows  straighter 
until  at  3  it  reaches  a  straight  line  for  a  very  short 
distance,  (d.)  It  is  symmetrical  in  parts  with  respect  to 
the  axis  of  the  cylinder,  and  to  lines  perpendicular  to  the 
axis  so  that  the  curve  from  o'  to  3  is  a  unit  which  is 
repeated  throughout  the  path  of  the  point. 

If  the  pitch  is  lessened,  the  curve,  at  the  contour 
elements  of  the  cylinder,  grows  sharper,  and  at  the  middle 
of  the  cylinder  straighter,  approaching  throughout 
straight  lines  oblique  to  the  axis  of  the  cylinder.  When  in 
the  ordinary  screw  the  pitch  is  exceedingly  small,  relative 
to  the  diameter  of  the  screw,  it  is  next  to  impossible  to 
draw  the  curve  correctly.  The  pitch  in  the  screw  means 
the  distance  between  the  turns  of  the  thread  measured 
axially  of  the  screw. 

64.  In  the  V  threaded   screw   three  curves  appear,  one 

theoretically  wound  around  a  larger  cylinder  at  the  crown 

_of  the  thread,  and  two  wound  around  a  smaller  cylinder, 

at  the  base,  or  root  of  the  thread.    In  the  square  threaded 

screw,  four  curves  appear,  two  at  the  crown  and  two  at 

the  root.    These  two  threads  are  shown  in  Figs.  43  and  44. 

The  contour  lines  of  the  V  thread  do  not  meet  at  the 

crown  of  the  thread  in  sharp  angles,  but  each  is  tangent  to 

the  curve  of  the  crown.    Again,  these  lines  do  not  meet  at 


110 


NOTES  ON  PRACTICAL  MECHANICAL  DRAWING. 
FIGURE   No.    48. 


WORKING  DRAWINGS. 


Ill 


112  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 

a  point  which  lies  on  the  cylinder  upon  which  the  root 
curve  is  theoretically  wound,  but  they  are  tangent  to  the 
root  curve,  and  cross  one  another  a  little  outside  of  it. 
These  facts  are  neglected  in  any  practical  drawing  of  the 
thread,  but  should  be  comprehended.  They  are,  unfortu- 
nately, too  often  incorrectly  shown  in  careful  drawings  of 
the  thread  and  in  well  known  text  books. 

The  diameter  of  a  screw,  as  dimensioned,  always 
stands  for  the  diameter  of  the  crown  line  of  the  thread ;  this 
does  not  indicate  the  strength  of  the  screw.  The  strength 
is  determined  by  the  diameter  at  the  root  curve  of  the 
thread,  being  the  minimum  cross  section  of  the  material 
of  which  the  screw  is  made. 

65.  Threads  are  shown  conventionally  unless  in  exceed- 
ingly rare  cases.  The  first  change  from  the  accurate 
thread  is  to  make  the  curves  straight  (as  shown  at  a  and 
b)  in  Fig.  45.  The  next  change,  in  the  case  of  the  V 
thread,  is  to  omit  the  saw  tooth  edge,  leaving  just  the 
longer  and  shorter  lines,  as  shown  at  e  and  /,  making  the 
limits  of  the  screw  a  cylinder.  Another  convention  is 
shown  also,  one  which  suggests,  in  a  way,  roundness  with 
a  sacrifice  of  the  screw  characteristic  as  at  g.  Square 
threaded  screws  are  relatively  rare,  and  there  is  no  partic- 
ular convention  in  use  to  represent  them  beyond  making 
one  thread  of  full  lines  and  dotted  limiting  lines  for  the 
others  as  at  c.  Sometimes  this  is  done  in  the  V  thread. 

The  lines  of  the  thread  have  a  slight  inclination 
upward  toward  the  right ;  the  direction  of  the  slant  of  the 
lines,  in  all  positions  of  the  screw,  can  be  ascertained  in 
this  way  by  looking  in  the  direction  of  the  axis  of  the 


WORKING  DRAWINGS. 
FIGUBE    NO.    45. 

6.  c. 


113 


screw.  For  left  handed  threads,  which  are  rare,  the  slant 
is  upwards  toward  the  left.  The  tap  for  a  screw  (see  Fig. 
44),  if  shown  in  section,  will  have  its  lines  the  reverse  of 
those  in  the  screw,  because  it  is  the  duplicate  of  the  curves 
on  the  rear  half  of  the  screw,  which  in  the  latter  are  not 
seen. 

In  ordinary  drawing,  of  course  the  pitch,  as  conven- 
tionally treated  in  Fig.  45,  is  not  measured  but  estimated. 


66.  The  Whitworth  standard  has  an  angle  of  55° 
between  the  sides  of  the  thread.  The  crown  and  root  of 
the  thread  are  both  rounded  off.  The  amount  taken  from 
the  crown,  and  that  added  to  the  root  of  the  thread,  being 
equal  to  one-sixth  of  the  total  depth  of  the  thread.  Let 
D'=  diameter  at  the  bottom  of  the  thread,  D  =  outside 
diameter  of  the  thread,  and  N  =  number  of  threads  per 
inch;  then  D  =  D'  —  L  2-^Q6°  (see  Fig  46  a). 


114  NOTES   ON   PRACTICAL  MECHANICAL  DRAWING. 

FIGURE  No.   46. 

a.  b. 


67.  The  U.  S.  standard  proportions,  devised  by  the  late 
William  Sellers  of  Philadelphia,  has  an  angle  of  60°  be- 
tween the  sides  of  the  thread.    The  crown  and  root  are  cut 
off  flat;  the  amount  added  at  the  root  being  equal  to  that 
taken  from  the  crown;  the  depth  of  the  flattened  face 

being  equal  to  one-eighth  of  the  depth  of  the  thread. 

1  299 
Using  the  notation  as  given  above,  D  =  D'  —    "^      (see 

Fig.  466). 

68.  There  are  other  forms  of  thread  occasionally  used 
besides  the  V  and  square  thread.    The  buttress  thread, 
for  example,  is  shown  in  Fig.  46,  at  c.    It  is  used  where 
the  screw  is  a  transmitter  of  power  or  to  resist  force  in  one 
direction.    A  screw  to  transmit  motion  may  have  a  short 
or  steep  pitch  according  to  the  speed  of  the  screw.    If  the 
speed  is  rather  great,  and  yet  it  is  desired  to  keep  the 
screw  strong,  or  even  for  the  latter  reason  alone,  it  may 
have  a  double  thread  or  a  triple  thread.    Thus,  for  one 


WORKING  DRAWINGS.  115 

revolution  of  the  screw,  it  will  travel  axially  two  times  the 
pitch,  or  three  times  the  pitch,  etc.  An  illustration  of  a 
screw  with  steep  pitch,  to  give  relatively  large  axial 
motion,  is  shown  in  the  thread  on  the  spindle  of  some 
valves.  There  is  even  a  certain  point  which  can  be 
reached  in  the  pitch  of  a  screw  thread,  that  longitudinal 
pressure  of  the  screw  bearing  against  the  thread  will  turn 
it.  -  This  is  illustrated  in  the  self-acting  screw  drivers. 

A  truncated  V  thread  is  one  in  which  the  crown  and 
root  have  been  very  materially  flattened.    It  is  a  kind 
used  in  the  spindles  of  some  valves,  as  before  mentioned 
A   form  of   truncated  V   thread,  known  as  the  Powell 
thread,  is  shown  in  Fig.  46,  at  d. 

69.  Bolt  heads  and  nuts  are  almost  universally  made  of 
the  hexagonal,  or  square  form,  so  as  to  be  convenient  to 
grip  with  a  wrench.  The  hexagonal  form  is  preferable, 
because  in  cramped  places  the  hold  of  the  wrench  can  be 
changed  after  turning  through  an  angle  of  60°  (see  Fig.  48. 
The  sizes  of  the  heads,  both  hexagonal  and  square,  are 
universally  standard  for  those  in  common  use.  Bolts  are 
either  cast,  cut  or  drop  forged.  The  sizes  are  determined 
as  follows:  Let  d  =  the  diameter  of  the  bolt,  D  the 
diameter  of  the  head,  then  the  formula  is  D  =  lJd  +  4". 
D  is  the  true  diameter  of  the  hexagonal  and  square  forms, 
namely,  the  perpendicular  distance  between  the  middle  of 
opposite  faces.  It  is  taken  this  way  so  that  the  wrench 
for  either  will  be  the  same. 

The  heads  are  not  left  in  the  prismatic  form,  exactly, 
but  are  chamfered.  The  under  side  of  the  head  is  left  flat. 
In  nuts,  both  hexagonal  faces  are  sometimes  chamfered. 


116  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 

A  nut,  that  is  to  tighten  down  on  a  flat  surface,  will  work 
better  into  place  without  cutting  the  material,  if  its  corners 
are  rounded.  To  get  the  chamfer,  the  bolt  is  put  in  the 
lathe,  and  the  cutting  tool  set  at  45°  to  the  axis  of  the  bolt, 
and  the  head  cut  until  all  the  edges  are  removed.  The 
surface  of  the  cut  is  a  cone ;  the  intersections  of  the  plane 
surfaces  of  the  head  with  this  cone  give  hyperbolas,  very 
short  arcs  however,  differing  so  slightly  from  the  circular 
that  never  in  practice  would  they  be  drawn  accurately. 
In  finished  bolt  heads,  the  dimensions  are  somewhat  less 
than  the  formula,  being  D  =  :  sl£d  +  iV.  The  height  of  a 
bolt  head  and  that  of  the  nut  vary  with  the  diameter  of  the 
bolt,  but  are  generally  drawn  equal  to  it,  Fig.  47  shows  a 
jtable  of  useful  facts  concerning  bolts,  etc.  • 

Fig.  48  shows  the  customary  method  of  drawing  the 
hexagonal  bolt  head.  The  lines  are  self  explanatory. 
There  are  two  forms  of  hexagonal  heads,  the  rounded  and 
the  square,  The  former  is  shown  in  the  figure  and  is  a 
cone  cut  by  seven  planes,  six  for  the  sides  and  one  for  the 
top  of  the  head. 

Bolt  heads  and  nuts  should  always  be  shown  alike  in 
position  of  a  drawing.  The  principal  view,  if  of  the  side 
of  a  hexagonal  bolt,  should  show  three  faces,  of  a  square 
bolt  head,  two.  If  only  one  view  of  a  bolt  is  shown,  it 
should  be  that  showing  three  faces  of  the  hexagonal  or 
two  of  the  square  headed. 

If  a  lock  nut  is  used  its  height  may  be  taken  as  one- 
half  the  diameter  of  the  bolt. 

In  dimensioning  standard  bolts,  it  is  customary  to  give 
only  the  diameter  of  the  bolt,  the  length  under  the  head 
and  the  length  which  is  threaded,  measuring  from  the  tip 


WORKING  DRAWINGS. 


117 


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118  NOTES   ON  PRACTICAL   MECHANICAL  DRAWING, 


FIGURE    No.    48. 


A=  D 

B=  varies  from  D, 
see  table. 
p+ris  for 
finish. 
R,  to  be  determined 


Nut 


WORKING  DRAWINGS.  119 

of  the  bolt,  unless  the  bolt  has  a  flat  or  countersunk  form 
of  head  in  which  the  'over  all'  is  the  required  dimension  of 
length. 

7O.     Bolts   and   screws   arc    variously   named    according 
to  the  functions  they  perform. 

An  ordinary  bolt  and  nut  is  generally  used  to  fasten 
two  or  more  pieces  together,  may  be  of  any  length  and 
threaded  any  length,  It  may  be  rough  or  finished.  It 
may  or  may  not  have  two  washers  one  under  the  nut 
and  one  under  the  head  to  form  good  bearing  surfaces. 
Finally,  it  may  have  any  one  of  a  variety  of  shaped  heads. 

A  machine  bolt  is  one  having  the  characteristics  of  an 
ordinary  bolt  as  well  as  others,  except  that  it  is  finished  all 
over  and  the  head  and  nut  are  consequently  smaller  in 
dimensions  than  those  in  rough  bolts. 

The  various  forms  of  heads  to  bolts,  excluding  the  hexa- 
gonal or  square  forms,  are  shown  in  Fig.  49,  with  the 
standard  proportions  in  common  use. 

A  tap  bolt  is  used  on  the  rougher  classes  of  machine 
work  usually,  to  fasten  two  or  more  pieces  together 
without  the  aid  of  a  nut,  namely,  by  tapping  into  one  of 
the  pieces.  It  should  not  go  down  to  the  bottom  of  the 
tapped  hole.  It  is  usually  threaded  throughout  its  length, 
although  this  is  not  invariable. 

A  cap  bolt  or  cap  screw  is  a  form  of  tap  bolt,  so  named 
from  its  function  in  holding  down  caps  or  covers.  It  is 
usually  threaded  for  three-quarters  of  its  length,  in  the 
smaller  sizes. 

A  stud  bolt  is  one  which  is  screwed  into  a  tapped  hole 
in  one  piece,  and  after  anqther  piece  has  been  slipped  over 


120 


NOTES  ON  PRACTICAL  MECHANICAL  DRAWING. 


Fl  GURB     No  .    49. 


Fillister  Head. 


Button  Head.       Counter  Sunk.         Collar  Head. 

f 


T   Ttrl 


id 


Tap  Bolt.  Cap  Bolt.  Stud  Bolt.  Set  Screw. 


Bolt  of  Unifon 
Strength. 

1 

j 

j 

—  U 

g 

g 

—  —  — 

=5 

^m^^ 

M^ 

it,  a  nut  is  screwed  on  to  hold  the  whole  together.  The 
bolt  should  not  screw  down  to  the  bottom  of  the  tapped 
hole,  the  depth  of  the  hole  should  moreover  be  equal  to 
at  least  one  and  one-half  times  the  diameter  of  the  bolt. 
The  smooth  part  of  the  bolt  should  be  less  in  length  than 
the  thickness  of  the  piece  screwed  down  over  it. 

A  set  screw  is  one  which  holds  another  piece  rigid  by 
pressure  against  its  point,  such  as  a  screw  through  a 
collar  holding  it  fast  from  turning  upon  a  shaft.  There 
are  various  forms  of  points  to  set  screws,  generally  square 
heads.  They  are  usually  threaded  throughout  their  length. 

In  nice  work  on  machine  bolts,  frequently  an  annular 
groove  is  cut  underneath  the  head  so  as  to  insure  the  bolt 
going  in  tight  and  close  to  the  head. 


WORKING  DRAWINGS.  121 

If  a  bolt  is  desired  of  uniform  strength,  the  shank  or 
smooth  part  will  be  made  equal  in  diameter  to  that  at  the 
base  of  the  threads. 

There  are  other  specially  named  bolts  such  as  eye 
bolt,  hook  bolt,  expansion  bolt,  etc.,  which  can  be  found 
described  in  the  hand  books.  Fig.  49  shows  the  various 
forms  of  bolts  above  enumerated  and  which  are  the  more 
common. 

There  are  other  specially  named  bolts  according  to  the 
the  special  uses  they  are  put  to,  as:  T  headed  bolts, 
having  two  faces  of  the  head  coincident  with  a  square 
neck  of  the  diameter  of  the  bolt  or  else  tangent  to  the 
shank.  It  is  used  where  there  is  not  room  enough  to  use  a 
square  or  hexagonal  headed  bolt.  A  hook  bolt,  a  bolt  of 
square  shank  and  turned  at  the  end  to  catch  on  a  ledge, 
used,  for  example,  in  fastening  hangers  to  flanged  beams. 
Expansion  bolt,  one  used  to  attach  parts  to  stone,  or 
concrete  work;  it  has  various  forms,  chiefly,  tending  to 
spread  out  at  the  end  and  fill  a  tapered  hole  larger  at  the 
inner  end.  One  form,  to  go  into  wood  work,  is  split  so 
that  when  forced  in,  it  spreads  out.  Anchor  bolt,  used 
to  hold  heavy  bodies  to  stone  or  concrete  foundations, 
similarly  to  an  expansion  bolt,  except  that  it  holds  by 
means  of  a  nut  and  washer,  the  latter  being  unusually 
large  in  proportion  to  the  diameter  of  the  bolt.  Eye  bolt, 
having  the  head  end  turned  into  an  eye  or  loop,  generally 
of  thickness  equal  to  the  diameter  of  the  bolt. 

71.  A  rivet  is  a  permanent  fastening  usually  used  to 
connect  two  or  more  thin  plates.  They  are  short  and  the 
shape  of  their  head  gives  them  their  name.  The  rivet 
consisting  simply  of  a  head  and  shank,  is  put  in  place, 


122 


NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 


either  hot  or  cold,  generally  the  former,  and  the  second 
head  is  formed  by  upsetting  with  a  fool  especially  con- 
structed. Rivets  are  now  put  in  place,  when  in  large 
numbers,  by  means  of  a  pneumatic  riveter  which  auto- 
matically forms  the  head,  when  in  place.  Fig.  50  shows 
some  of  the  chief  forms  of  rivet  heads  and  the  proportions 
in  common  use. 

FIGURE  N  o.  50. 
Button  Head        SnaPHeadOnlCal        Steeple  Pointed  Head.  Countersunk  Head. 


72.     General  directions  for  the  treatment  of  problems  to 

follow: 

Draw  the  center  lines  first  and  next  the  centers  of  arcs  and 
curves  tangent  to  straight  lines;  that  is,  make  the  outline  or 
contour  forms,  except  in  the  case  of  very  small  curves  or  fillets, 
determined  by  the  curves  to  which  they  are  tangent.  In  con- 
struction, the  exact  location  of  these  centers  may  be  very 
important.  After  the  centers  are  located  and  the  curves  drawn, 
enclose  the  remaining  part  of  the  views  by  straight  lines,  and  so 
on  to  the  finish. 

To  be  exact  in  the  tangency  of  curves  to  straight  lines, 
and  of  curves  to  each  other,  observe  that  the  marks  made 
in  the  paper  by  the  needle  point  centers  are  as  small  as 
possible. 

Indicate  centers  for  all  arcs,  other  than  very  small  ones 
like  fillets,  by  at  least  two  center  lines  crossing  each  other 
at  right  angles  at  the  center,  say  i  of  an  inch  long. 


WORKING  DRAWINGS.  123 

Dotted  lines  can  be  made  quite  explanatory  of  forms, 
The  thickness  of  a  dotted  line  should  be  no  greater  than 
that  of  the  solid  outlines,  in  fact,  it  is  well  to  make  it 
slightly  lighter,  for  the  short  dots  are  likely  each  to  be 
thicker  than  a  continuous  line  made  with  the  same  setting 
of  the  pen.  A  dotted  line  is  not  ideally  composed  of  dots, 
but  of  short,  uniform  and  evenly  spaced  strokes.  The 
uniformity  of  dotting  is  a  thing  which  sets  off  a  drawing. 
Dotted  construction  should  look  intelligible  always.  To 
effect  this,  several  points  should  be  observed: 

(a.)     The  angles  of  sharp  corners  should  be  con- 
nected strokes. 

(&.)     Where  the  dotted  line  crosses  solid  lines, 

and  is  not  related  to  them  by  identity  of  form 

or  material,  the  dots  should  not  stop  at,  but 

cross,  these  lines. 

(c.)    Where  dotted  lines  properly  end  at  solid 

lines,  the  dots  should  touch  the  lines. 
W. )    In  the  dotted  lines  in  either  of  the  above 
cases,  the  dots  marking  the    angles,  or  those 
crossing  solid  lines  or  meeting  to  end  at  solid 
lines,  can  well  be  made  longer  than  the  dots 
of  the  rest  of  the  line,  even  twice  the  length. 
Dotting,  in  brief,  should  clearly  define  the  forms  by 
accentuating  with  larger  dots  the  salient  things  to  be 
brought  out. 

73.    Miscellaneous  problems. 

-^-Problem  1.  Draw  a  plan  and  elevation  of  the  form 
shown  in  Fig.  51,  adding  the  dimensions  as  given  and 
placed  in  similar  positions  on  the  views. 


NOTES  ON  PRACTICAL  MECHANICAL  DRAWING. 
FIGURE    No.    51. 


1 


Draw  first  the  plan  view,  laying  out  the  center  line,  scaling  the 
length  over  all,  and  the  width  of  the  view.  Next,  lay  off  the 
shorter  horizontal  distances,  preferably  upon  the  center  line, 
marking  continuously  from  the  scale,  then  the  vertical  measure- 
ments, either  side  of  the  center  line  at  the  points  marking  the 
horizontal  distances.  Line  in  the  view,  horizontal  lines  first  and 
then  vertical  lines. 

Lay  out  the  elevation  in  a  similar  manner  to  the  plan.  Put 
on  the  limiting  lines,  dimension  lin'es,  arrow  heads  and  figures  in 
the  order  named.  The  dimensions  occupy  relatively  the  proper 
place  upon  the  figures  that  they  should  in  the  working  drawing. 

In  inking,  rule  the  horizontal  lines  of  all  the  views  first, 
beginning  at  the  top  and  going  down.  Rule  the  vertical  lines 
next,  including  dotted  lines  and  invisible  edges.  Rule  the  limiting 
and  dimension  lines  next,  and  lastly  put  in  arrow  heads  and 
dimension  figures  in  the  order  named. 

Problem  2.  Draw  a  plan  and  elevation  of  the  form 
shown  in  Fig.  52,  adding  the  dimensions  as  given. 


WORKING  DRAWINGS. 


125 


126  NOTES   ON   PRACTICAL   MECHANICAL  DRAWING. 

Draw  first  the  plan,  laying  out  the  center  line,  scaling  the 
length  over  all,  and  the  width  of  the  view.  Next,  lay  off  the 
shorter  horizontal  distances,  preferably  upon  the  center  line, 
marking  continuously  from  the  scale,  then  the  vertical  measure- 
ments, either  side  of  the  center  line  at  the  point  marking  the 
horizontal  distances.  Line  in  the  view,  horizontal  lines  first  and 
then  vertical  lines. 

Lay  out  the  elevation  in  a  similar  manner  to  the  plan.  Put  on 
limiting  lines,  arrow  heads  and  figures  in  the  order  named. 

In  inking,  rule  the  horizontal  outlines  of  all  the  views' first, 
beginning  at  the  top  and  going  down.  Rule  the  vertical  outlines 
next,  including  dotted  lines  or  invisible  edges.  Rule  the  limiting 
and  dimension  lines  next,  and  lastly,  put  in  arrow  heads  and 
dimension  figures  in  the  order  named. 

Problem  3.  Draw  plan,  elevation  and  end  view  of  the 
form  shown  in  Fig.  53,  adding  the  dimensions  given. 

Draw  first  the  plan  of  the  form,  laying  out  center  lines,  scaling 
the  length  over  all  and  the  width  of  each  end,  then  enclosing  by 
lines.  Draw  the  elevation  next,  and  then  either  end.  After  this 
put  ont  he  dimension  lines,  limiting  lines  and  arrow  heads,  lastly 
the  dimension  figures. 

In  inking,  rule  the  horizontal  lines  of  all  the  -views  first, 
beginning  at  the  top  and  going  down.  Rule  the  vertical  outlines 
next,  finally  the  oblique  lines.  Next  rule  the  limiting  and 
dimension  line,  and  lastly  put  in  arrow  heads  and  dimension 
figures  in  the  order  named. 

Problem  4.  A  flange  for  outlet  and  inlet  pipes  for  a 
hydraulic  riveting  machine.  See  Fig.  54.  The  pipes 
screw  into  the  tapped  holes  shown.  Copy  the  views 
shown,  making  full  size.  This  figure  shows  the  proper 
weight  of  line  for  a  working  drawing. 

Draw  the  main  center  lines  of  the  upper  or  plan  view  first, 
continuing  the  vertical  one  down  to  the  elevation.  Next  draw  the 
minor  center  lines  of  the  plan,  then  close  in  the  plan,  smaller 
circles  first,  then  the  larger  and  the  straight  lines  last.  Draw  the 
elevation  from  the  plan,  making  the  upper  and  lower  horizontal 


WORKING  DRAWINGS. 


127 


128 


NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 
FIG  TIRE     NO.     54. 


* 

^8 

1 

i     I!*-'^ 

t  VI'    ' 

:    v 

\\ 

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1 

1 

i's  t    ^ 

t 

1  1 

i    i 
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limiting  lines  first,  then  projecting  down  from  the  plan.     Put  the 
dimensions  on  as  on  the  figure. 

When  ready  to  ink,  put  in  the* small  arcs  with  the  bow  pen, 
then  the  larger  with  the  compass,  and  lastly  the  straight  lines. 
Put  in  the  limiting  lines,  dimension  lines,  arrow  heads,  and  figures 
in  the  order  named. 

Problem  5.  Draw  an  under  plan,  an  elevation  and  an 
end  view  of  the  form  shown  in  Fig.  55,  adding  the  dimen- 
sions as  given. 

Draw  first  the  plan  view,  laying  out  the  center  lines,  vertical 
and  horizontal,  scaling  the  length  over  all  and  the  width  of  the 
view.  Next  locate,  centers  for  and  draw  all  arcs  of  circles, 


WORKING  DRAWINGS. 


129 


*VNI 

xi-Aw  "\frv-*- 


130  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 

connecting  same  by  tangent  and  enclosing  lines.  Draw  the 
elevation,  then  the  end  view  from  the  plan  following  same  general 
procedure.  Put  in  the  dimensions  as  on  the  figure  in  the  same 
relative  positions,  except  show  radii  upon  a  radial  dimension  line, 
lettered  R  or  Rad. 

When  inking  put  in  the  arcs  of  circles  first,  in  all  views,  then 
the  straight  lines,  horizontal  and  vertical  in  turn.  The  limiting 
lines,  dimension  lines,  arrow  heads  and  figures  go  in  last  in  the 
order  named. 

Problem  6.  Draw  a  plan,  an  elevation  and  an  end 
view  of  the  form  shown  in  Fig.  56,  adding  the  dimensions 
as  given. 

Draw  first  the  end  elevation,  which  is  a  view  looking  toward 
the  left,  laying  out  the  center  lines,  scaling  the  length  and  height 
over  all  and  constructing  either  side  of  the  center  line.  Locate 
the  centers  for,  and  draw  all  arcs  the  first  lines  drawn,  connecting 
same  by  tangent  and  enclosing  lines.  Draw  the  front  elevation 
and  then  the  plan  next  following  the  same  general  procedure 
except  that  the  plan  will  have  two  axes  of  symmetry.  Put  in 
the  dimensions  as  on  the  figure  in  the  same  relative  positions, 
except  show  the  radii  upon  radial  dimension  lines,  lettered  R  or 
Rad. 

When  inking  put  in  the  arcs  of  circles  first  in  all  views,  then 
the  straight  lines,  horizontal  and  vertical  in  turn.  The  limiting 
lines,  dimension  lines,  arrow  heads  and  figures  go  in  last  in  the 
order  named. 

Problem  7.  A  cross  section  of  a  P.  R.  R.  standard 
100-lb.  rail,  see  Figure  57.  Draw  the  view  from  the 
sketch,  full  size,  to  the  dimensions  shown.  It  is  an 
exercise  in  the  tangency  of  curves. 

Draw  the  vertical  center  line  first,  then  the  centers  for  the 
arcs  designating  the  web,  then  the  crown  of  the  rail,  and  the  base 
and  so  on,  locating  centers  in  the  penciling  carefully  by  free-hand 
circles  around  the  intersections  of  the  construction  lines.  Put  on 
the  dimensions  as  shown. 

When  ready  to  ink,  put  in  the  small  arcs  with  the  bow  pen, 
then  the  larger  with  the  compass  and  lastly,  the  straight  lines. 


WORKING  DRAWINGS. 


131 


132  NOTES   ON  PRACTICAL.  MECHANICAL.  DRAWING. 


FIGURE    No.    57. 


WORKING  DRAWINGS. 


133 


Show  the  plane  of  the  section  by  regularly  spaced  lines,  at  45°  to 
the  horizontal  and  about  one-sixteenth  of  an  inch  apart  at  the 
least,  the  weight  of  the  line  to  be  slightly  lighter  than  the  outline. 
Put  in  the  limiting  lines,  dimension  lines,  arrow  heads  and  figures 
in  the  order  named. 

FIGURE    No.    58. 


Problem  8.     Make  the  necessary   working    drawing 
views  to  show  the  stop  lever  in  Fig.  58. 

Draw  the  horizontal  and  oblique  center  lines  of  both  views 
first.  Next,  draw  the  central  boss  and  left  hand  end  of  the  lower 
view  or  elevation.  Then  draw  the  fork  of  the  plan  view  and 
project  down  to  the  elevation.  Finish  the  elevation  then  the  plan. 
Put  the  dimensions  on  to  correspond  with  their  general  positions 
on  the  sketch. 

When  ready  to  ink,  draw  the  circular  arcs  first,  then  the  hori- 
zontal, vertical  and  oblique  lines  in  order.  Put  in  limiting  lines, 
dimension  lines,  and  arrow  heads  and  figures  in  the  order  named. 

Problem  9.    An  overhung  crank  for  an  engine.    Draw 
a  front  and  side  view  from  the  sketch  in  Fig.  59,  full  size. 


134  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 


FIGURE    No.   59. 


WORKING  DRAWINGS.  135 

Call  the  front  view  the  one  looking  in  the  direction  of  the 
shaft;  this  should  be  drawn  first 

Note  the  conventional  method  of  showing  a  break  in  a 
shaft  by  aid  of  the  small  detail  at  the  left  of  the  figure. 
The  curved  part  is  sometimes  made  with  the  curved  rule, 
but  this  is  not  at  all  necessary.  The  small  detail  at  the 
right  shows  the  demensions  which  could  not  be  repre- 
sented on  the  perspective  sketch. 

The  sectioning,  or  conventional  method  of  showing 
the  cut  surface  should,  in  all  cases,  be  ruled  by  equally 
spaced  lines  somewhat  lighter  than  the  general  outlines, 
about  one-sixteenth  of  an  inch  apart  in  this  problem. 

Problem  1O.  Draw  the  front  view  and  side  view  of 
the  rocker  arm  as  shown  by  perspective  sketch  in  Fig. 

60.  Call  the  front  view  the  one  looking  in  the  direction  of 
the  shaft  at  the  top. 

This  form  will  show  the  advantage  of  developing  parts 
of  several  views  simultaneously.  The  front  view,  includ- 
ing the  split  collar,  and  what  is  below,  is  best  drawn  first; 
that  which  is  above  the  split  collar,  including  the  tighten- 
ing bolt,  should  be  drawn  in  the  end  view  first.  Put  in 
small  rounded  edges  or  fillets  last  in  pencil,  but  first  in 
inking. 

Problem  11.    A  discharge  cap  for  a  pump,  see  Fig. 

61.  Make  the  views  shown  by  sketch  to  a  scale  of  three 
inches  to  the  foot,  and  in  proper  position,  render  the  right 
hand  half  of  both  side  and  end  views  in  section. 

*  Problem  12.  A  brake  shoe,  see  Fig.  62.  Make  a 
plan,  elevation  and  side  view  of  the  form  shown  by  sketch, 
to  a  scale  of  three  inches  to  the  foot.  Also  make  a  section 

*  From  Rautenstrauch  &  Williams'  'Machine  Drafting.' 


or 

Of 


NOTES  ON  PRACTICAL,  MECHANICAL  DRAWING. 
FIGURE  No.  60. 


|4  bore 


WORKING  DRAWINGS. 


137 


i^X.    ..r'T"^-^ 


138 


NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 


F  I  QTJRB    N  O. 


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WORKING  DRAWINGS. 
FIGURE  No.  68. 


with  J|> 
bored  holes 

Curves  of 

braces, 

optional. 


looking  downward  at  the  center  line  of  car  wheel.  Put  on 
all  dimensions  shown. 

Problem  13.  Make  a  pla^^ekrVaSonand  end  view  of 
the  bracket  shown  inj£igr1$3^  to  a  scale  of  three  inches  to 
the  foot.  Put  ontdfneeessary  dimensions. 

Problem  14.  Make  a  working  drawing  of  the  pillow 
block  as  sketched  in  Fig.  64,  to  a  scale  of  four  inches  to 


140  NOTES   ON   PRACTICAL  MECHANICAL  DRAWING. 

the  foot.  Make  also  a  longitudinal  section  through  the 
center.  Put  on  all  dimensions  as  shown. 

Problem  15.  Make  a  drawing  of  the  cylinder  head 
and  stuffing  box  as  sketched  in  Fig.  65  to  a  scale  of  half 
size.  Draw  in  the  three-quarter  inch  bolts  and  nuts  on  the 
left  hand  half  of  the  front  view,  facing  all  nuts  the  same 
way.  Draw  the  front  view  first,  taking  sizes  where 
necessary  from  the  side  view.  Put  on  all  the  dimensions 
as  shown. 

Problem  16.  A  bench  griader.  Make  an  elevation 
complete  from  the  sketchizrTig.  66  of  the  bench  grinder, 
also  a  plan  view  and^ena  view  and  complete  longitudinal 
section.  Put  on/all  the  dimensions  shown,  distributing 
them  properly^etween  the  views. 

Problem  17.  A  bench  grmder.  Make  a  set  of  work- 
ing drawings  complete  of  aJPparts  of  the  bench  grinder  as 
sketched  in  Fig.  66,  apa  to  a  suitable  scale.  Put  on  all 
the  necessary  dimensions  and  tabulate  a  bill  of  materials. 

Problem  18.  Make  a  drawing  of  the  engine  bed  as 
sketched  in  Fig.  67,  to  a  scale  of  one-fourth  size.  Put  on 
all  dimensions,  where  possible  in  their  proper  place,  but  if 
there  is  not  room,  place  to  one  side  and  refer  to  them  by 
direction  lines  as  shown  here  and  there  in  the  sketch. 

Make  a  central  longitudinal  section  of  the  bed. 

Problem  19.  Make  a  drawing  of  the  'StancJartT  Pile 
Bridge'  construction  shown/by  sketch  in  Fig^6Sa  and  686, 
and  as  used  by  the  C.  Br&  Q.  E.  R.  Make  it  to  a  scale  of 
one-fourth  inch  to  jthe  foot,  and  arrange  the  views  appro- 
priately. 


WORKING  DRAWINGS. 


141 


FIGURE    No.    64. 


142 


NOTES  ON  PRACTICAL,  MECHANICAL  DRAWING. 


-J-.-y-j— H-£-r-V -1 ^ 


WORKING  DRAWINGS. 


143 


144 


NOTES  ON  PRACTICAL  MECHANICAL  DRAWING. 


WORKING  DRAWINGS. 


145 


146 


NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 


WORKING  DRAWINGS.  147 

Problem  2O.  Make  a  drawingj^f-thlf^Tixed  End 
Casting7  used  by  the  Illinois  CejitraTR.  R.  on  their  standard 
177 '_6' '  'Through  Finnan*  and  as  sketched  in  Fig.  69. 
Make  it  to  a  scale^or  one-eighth  size.  Put  on  all  dimen- 
sions 

Problem  21,  Locomotive  piston  head.  Make  a  work- 
ing drawing  from  the  sketch  in  Fig.  70  to  a  scale  of  six 
inches  to  the  foot. 

Problem  22.  Make  a  drawing  of  the  fly  wheel  shown 
by  sketch  in  Fig.  71,  to  a  scale  of  one  and  one-half 
inches  to  the  foot.  Draw  at  least  half  the  wheel  in  both 
views. 

*  Problem  23.  Make  a  drawing  of  the  locomotive 
driving  wheel  as  sketched  in  Fig.  72,  to  a  scale  of  two 
inches  to  the  foot.  Make  also  a  section  of  the  wheel  at 
right  angles  to  that  shown. 

Problem  24.  Bench  vice.  Make  a  complete  set  of. 
working  drawings  from  the  sketches  in  Fig.  73,  also  a  set 
of  assembly  views.  The  figure  illustrates  arrangement  in 
working  drawing. 


*  From  The  Locomotive  Dictionary. 


148 


NOTES    ON   PRACTICAL  MECHANICAL  DRAWING. 


FIGURE  No. 


WORKING  DRAWINGS. 


149 


150 


NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 


WORKING  DRAWINGS. 


151 


152 


NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 


CHAPTER    VI. 
GEOMETRICAL    DRAWING. 

74.     Geometrical  Drawing  vs.  Mechanical  Drawing. 

Use  all  the  mechanical  aids  that  are  available  to  get 
constructive  results  in  a  drawing,  provided  the  processes 
do  not  involve  too  great  an  expenditure  of  time.  Geo- 
metrical processes,  by  their  very  multiplicity  of  steps, 
open  the  way  for  errors,  and  are  practically  more  likely  to 
result  in  faulty  construction  than  if  mechanical  aids  were 
used.  But  there  are  a  few  fundamental  processes  which 
every  draftsman  ought  to  known  and  there  are  some 
mechanical  equivalents,  also.  As  for  the  many  geometrical 
constructions  of  a  more  or  less  simple  form,  the  student  is 
recommended  to  consult  the  various  hand  books. 

Parallel  lines  are  more  easily  obtained  by  mechanical 
methods.  The  T  sq.  and  also  the  T  sq.  and  triangles 
taken  together,  show  the  simplest  cases.  For  others  use 
either  a  straight  edge  and  triangle,  or  two  triangles.  Place 
an  edge  of  the  triangle  to  the  given  line,  and  the  straight 
edge  or  the  other  triangle  against  either  of  the  other  edges. 
The  first  triangle  moved  in  either  direction  will  present 
parallel  sides. 

Perpendiculars  and  verticals  mean  two  different  things. 
Perpendicular  is  a  relative  term  and  means  that  one  line  is 
at  90°  to  the  other,  or  normal,  no  matter  what  the  direction 
of  either  line.  Vertical,  in  a  drawing,  means  a  line  which 
is  perpendicular  to  a  horizontal  one  only.  In  space  it  is  a 


154  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 

normal  to  a  horizontal  plane,  or  in  other  words,  to  the 
earth's  surface. 

Perpendiculars  can  be  made  most  readily  with  the 
triangles  and  T  sq,  or  straight  edge.  In  the  case  of 
oblique  lines,  place  one  triangle  against  the  given  line  and 
move  it  against  the  other  triangle,  as  for  parallel  linec, 
until  it  is  a  short  distance  away,  then  use  the  second 
triangle  against  the  first  so  that  the  perpendicular  drawn 
can  be  made  to  intersect  and  cross  the  first,  if  necessary. 

It  is  a  mistake  to  draw  the  perpendicular  when  the 
first  triangle  is  in  contact  with  the  given  line. 

Eight  angles  can  be  divided  readily  into  halves  and 
thirds  by  means  of  the  45°  and  30°  and  60°  triangles,  either 
with  the  assistance  of  a  T  sq.,  or  without,  by  the  process 
just  described  for  perpendiculars  and  verticals.  Hence,  a 
circle  can  be  divided  into  four,  eight  or  twelve  parts,  and 
by  bisecting  one  angle  a  new  base  can  be  obtained  for 
halving  all  the  angles  and  doubling  the  number  of  the 
above  mentioned  divisions. 

Tangency  in  geometry  means  identity  of  direction  at  a 
common  point.  Identity  of  direction  also  means  that  the 
common  tangent  to  two  curves  is  a  normal  to  the  radius 
of  curvature  of  each  at  the  point  of  tangency. 

Since  in  geometry  lines  have  no  thickness,  it  follows 
that  two  lines  in  a  drawing  that  are  to  be  tangent  to  each 
other  should  be  made  not  osculating  lines,  but  identical, 
that  is,  the  thickness  of  the  lines  at  the  point  of  tangency 
should  be  that  of  the  thickest  line  only  which  is  used. 

75.    To  draw  a  tangent  to  an  irregular  curve  at  a  point 
on  the  curve.     See  Fig.  74. 


GEOMETRICAL  DRAWING  155 

FIGURE   No.  74. 


Through  T,  the  point  of  the  desired  tangent,  draw 
random  secants,  as  1,  2,  3,  4,  5,  etc.,  through  points  on 
the  curve.  With  T  as  a  center,  and  any  radius,  describe  an 
arc  to  cut  the  secants  prolonged.  On  each  secant  lay  off, 
from  its  intersection  with  the  circle,  a  distance  equal  to  the 
chord  length  of  the  secant  within  the  irregular  curve,  and 
measuring  on  the  same  side  of  the  circle  as  the  secant  with 
respect  to  the  point  T.  Draw  a  curve  through  these 
points.  Where  this  curve  cuts  the  auxiliary  circle,  is  a 
point  in  the  tangent. 

76.    To  rectify  an  arc  of  a  curve  or  of  a  circle  subtending 
a  small  angle.    See  Fig.  75. 

Let  BA  be  the  given  arc.  Prolong  the  chord  AB  to  O, 
making  OA  =  AB  -f-  2.  With  radius  OB  draw  an  arc  to 
cut  a  tangent  to  the  curve  at  A  in  C.  AC  will  be  the 


156 


NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 
FlGUKB    No.    75. 


desired  length. 
for  short  arcs. 


This  is  an  approximation,  and  useful  only 


77.    To  draw  an  arc  of  given  radius  tangent  to  two  given 
oblique  lines.     See  Fig.  76. 


FIGURE  No.  '76. 


Prolong  the  given  lines  to  meet  at  0.  With  O  as  a 
center,  and  the  given  radius,  describe  an  arc.  Parallels 
to  the  given  lines,  and  drawn  tangent  to  this  arc,  will  meet 
at  C,  from  which  perpendiculars  to  the  given  lines  give 
the  points  of  tangency,  C  being  the  center  of  the  arc. 


GEOMETRICAL  DRAWING. 


157 


78.    The  conies. 

The  conic  sections,  or  simply  conies,  appear  fre- 
quently in  mechanics  and  machine  construction.  They  are 
called  conic  sections  because  they  are  the  contour  forms  of 
plane  sections  of  a  cone  of  revolution.  A  cone  of  revolu- 
tion is  a  cone  formed  by  one  line  revolving  about  another, 
which  it  intersects,  and  with  which  it  maintains  a  constant 
angle. 

FIGURE    No .  77. 


A  circle  is  formed  by  cutting  the  cone  perpendicular  to 
the  axis,  as  a— a,  see  Fig.  77. 


158 


NOTE8   ON  PRACTICAL,  MECHANICAL  DRAWING. 


A  parabola  is  formed  by  cutting  the  cone  in  a  plane 
parallel  to  the  moving  line  as  6-6. 

A  hyperbola  is  formed  by  cutting  the  cone  in  a  plane 
making  a  less  angle  with  the  axis  than  the  moving  line, 
as  c-c. 

An  ellipse  is  formed  by  cutting  the  cone  at  any  other 
angle,  i.e.,  making  a  greater  angle  with  the  axis  than  the 
elements. 

Ellipses,  parabolas  and  hyperbolas  may  be  drawn  in 
several  different  ways.  A  few  of  the  more  common  and 
convenient  will  now  be  given: 


79.  To  draw  an  ellipse  by  the  focii  method;  to  draw  it  by 
the  principle,  in  other  words,  that  the  sum  of  the  focal 
radii  to  any  point  on  the  curve  is  a  constant,  see  Fig.  78. 
The  constant  is  equal  to  2a.  The  focal  radii  are  F  P  and 
F'P,  respectively. 


GEOMETRICAL    DRAWING.  159 

When  the  major  and  minor  axes  are  given,  the  focii 
may  be  obtained  as  follows ;  With  a  radius  equal  to  the 
semi-major  axis,  and  a  center  at  either  extremity  of  the 
minor  axis,  describe  arcs  to  cut  the  major  axis  in  points 
which  will  be  the  focii,  for  FY  +  YF'  =  2a.  To  find  any 
point  on  the  curve,  as  P,  take  any  radius  not  less  than 
X'F  or  XF',  and  with  center  at  F,  describe  an  arc  of  a 
circle ;  with  a  radius  equal  to  the  difference  between  2a, 
and  the  radius  just  taken,  and  a  center  at  F',  describe  an 
arc  to  intersect  the  first  one  at  P,  which  will  be  a  point  on 
the  curve.  There  are  three  other  points  on  the  curve,  cor- 
responding with  P,  and  which  are  symmetrical  with 
respect  to  the  axis,  hence,  the  practical  method  of  pro- 
cedure is  to  arbitrarily  divide  the  major  axis  between  the 
focus  and  the  center  of  the  ellipse  into  several  parts,  each 
to  give  two  radii  for  four  symmetrical  points  on  the  curve. 
With  each  radius  taken,  the  four  symmetrical  points  are 
obtained  by  striking  arcs  from  both  focii  above  and  below 
the  major  axis. 

For  careful  drawing,  more  points  will  have  to  be 
plotted  in  the  neighborhood  of  the  major  axis,  than  in 
that  of  the  minor.  It  is  well  to  find  a  group  of  symmetri- 
cal points,  as  just  described,  complete,  before  proceeding 
with  any  construction  for  other  points. 

8O.     To    construct    an    ellipse    by    the    method    of    the 
trammel. 

The  trammel  is  an  instrument  for  mechanically  con- 
structing an  ellipse,  not  very  successful  practically, 
because  of  its  lack  of  adaptability,  and  its  cumbersomeness, 
as  well  as  large  cost.  It  consists,  fundamentally,  of  two 


160 


NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 


tracks  or  guides  at  right  angles  to  each  other,  and  which 
constitue  the  major  and  minor  axes.  A  third  member,  an 
arm,  carries  a  marking  point,  while  two  wheels,  or  lugs, 
fastened  to  it  rigidly,  move  in  the  grooves  in  the  first  two 
members,  and  hence  constrain  the  moving  arm  so  that  its 
marking  point  goes  in  the  path  of  an  ellipse.  The  opera- 
tion can  be  more  readily  seen  after  a  description  of  its 
practical  equivalent,  see  Fig.  79. 

FIGURE   No.    79. 


Take  a  piece  of  paper  as  a  straight  edge,  and  mark  on 
it  a  point  P.  From  P  lay  off  a  distance,  Pa',  equal  to  a, 
and  also  a  distance,  P6',  equal  to  &.  Then  with  &'  touch- 
ing the  major  axis,  and  a'  the  minor  axis,  P  will  be  a 
point  upon  the  curve.  To  plot  points  then,  move  the 
straight  edge  around  into  as  many  positions  as  desired, 
and  for  each  point  plotted,  indicate  its  place  by  a  short 
stroke  along  the  straight  edge,  and  one  perpendicular  to  it 
at  P.  This  kind  of  stroke  will  identify  the  points  most 


GEOMETRICAL   DRAWING. 


161 


successfully.  This  method  of  plotting  an  ellipse  is  an 
excellent  one,  because  of  the  ease  with  which  the  points 
can  be  located,  where  wanted. 

81.     To  draw  an  ellipse  approximately  with  the  compass, 
See  Fig.  80. 

Fl  GIT  KB     NO  .     80. 


This  is  the  method  the  mechanical  draftsman  will 
alway  use,  where  possible,  and  it  is  a  very  good  substitute. 
There  are  two  ways,  the  following:  being  the  more  common: 

Draw  the  minor  auxiliary  circle,  it  will  cut  the  major 
axis  in  C.  Connect  B  and  A.  Lay  off  on  BA  from  B,  the 
distance  BC',=  AC.  Next,  bisect  the  line,  C'A,  and  pro- 
long the  bisector,  OO ' ,  to  meet  the  minor  axis  prolonged 
in  O'.  0'  is  the  center  for  an  arc  passing  through 
B,  which  approximates  the  ellipse.  From  the  point  in 


162  NOTES   ON   PRACTICAL  MECHANICAL  DRAWING. 

which  this  arc  touches  the  bisector,  00 ' ,  draw  an  arc  of 
another  circle,  passing  through  A,  which  has  its  center 
where  the  bisector  cuts  the  major  axis.  To  complete  the 
curve,  another  center  may  be  found  on  the  other  side  of 
the  major  axis,  and  symmetrical  with  0',  and  one  on  the 
other  side  of  the  minor  axis,  symmetrical  with  the  center 
C.  This  is  a  method  of  drawing  an  ellipse,  which,  of 
course  more  closely  simulates  the  true  curve,  the  nearer 
the  ratio  of  the  two  axes  is  equal  to  one.  If  one  has  any 
facility  in  free-hand  work,  it  is  recommended  that  a 
quadrant  be  sketched  in  roughly,  and  then  copied  as 
closely  as  possible  with  arcs,  and  using  as  many  centers 
as  needed  for  the  purpose.  The  ellipse  will  not  be  as  true 
as  if  plotted  by  points,  but  it  will  be  a  smooth  curve  and 
make  a  better  general  appearance  than  if  constructed  as 
first  directed. 

82.    To  draw  a  parabola  by  means  of  the  focus. 

A  parabola  is  defined  in  mathematics,  as  the  locus 
of  a  point  which  moves,  so  that  its  distance  from  a  fixed 
point,  called  the  focus,  is  equal  to  its  distance  •  from  a 
fixed  line,  called  the  directrix. 

Let  DD'  (Fig.  81)  be  the  directrix,  and  OF  at  right 
angles  to  it,  the  axis.  Let  F  be  the  focus.  Since  the 
distance  of  F  from  any  point  on  the  curve  is  equal  to  the 
distance  of  that  point  from  the  directrix,  to  find  any  point 
on  the  curve  as  P,  draw  a  line  parallel  to  DD'  at  any 
chosen  distance  from  it.  Then  with  this  same  distance  as 
a  radius,  and  F  as  a  center,  describe  an  arc  to  cut  the 
parallel  in  the  point,  P.  Two  such  points,  P  and  P',  will 
be  found  symmetrical  with  the  axis.  One  point  must  lie 


GEOMETRICAL    DRAWING. 


163 


on  the  axis  half  way  between  the  focus  and  directrix, 
namely,  O,  which  is  called  the  vertex.  The  entire  curve 
is  symmetrical  on  its  axis. 


FIQUKK   No.   81. 


To  plot  a  large  number  of  points,  for  a  good,  smooth 
curve,  divide  the  axis,  arbitrarily,  into  a  number  of  points 
starting  at  the  vertex.  Through  these  draw  parallels  to 
the  directrix.  Then  with  radii  equal,  respectively,  to  these 
distances  from  the  directrix,  describe  arcs  from  the  focus 
as  a  center  to  cut  the  parallels  in  points  of  the  curve. 


83.     To  draw  a  hyperbola  by  means  of  its  focii. 

A  hyperbola  is  denned  in  mathematics  as  the  locus 
of  a  point  which  moves  so  that  the  ratio  of  its  distance 


164 


NOTES  ON  PRACTICAL  MECHANICAL  DRAWING. 


from  a  fixed  point,  called  the  focus,  to  its  distance 
from  a  fixed  line,  called  the  directrix,  is  a  constant  and 
greater  than  unity,  see  Fig.  82. 

FIGUKE    No.   82. 


We  shall  work  the  problem,  however,  by  the  geo- 
metrical principle  that  the  difference  between  the  focal 
radii  to  any  point  on  the  curve  is  a  constant.  Let  F  F'  be 
the  focii,  and  0  the  center.  Assume  the  vertices  of  the 
curve,  A  A',  at  equal  distances  from  0  on  the  axis  F'F. 
A  A'  is  also  the  constant  difference.  Take  any  point  on 
the  axis  a  distance  from  F'  greater  than  F'A  as  F'Q,  and 
with  F'  as  a  center  describe  an  arc;  then,  substracting  the 
constant  A 'A,  from  F'Q  take  the  remainder  as  a  radius, 
and  with  F  as  a  center  describe  an  arc  to  cut  the  first  one 


GEOMETRICAL   DRAWING. 


165 


in  points  of  the  curve  above  and  below  the  axis,  and  so 
proceed  for  as  many  points  as  desired. 

Now,  consider  that  hyperbola,  which  is  formed  by  a 
section  of  a  cone  parallel  to  its  axis,  it  can  be  easily  seen 
that  if  the  two  elements  of  the  surface  (positions  of  the 
moving  line),  which  are  parallel  to  the  plane  of  the  section, 
were  projected  on  the  plane  of  the  section,  the  curve 
would  approach  but  never  touch  them.  These  two 
elements  are  known  as  the  asymptotes  of  the  curve. 


FIGURE    No.   88. 


B 


0 


84.    To  draw  a  hyperbola  by  the  rectangle  method. 

This  is  a  method  which  is  associated  with  certain 
properties  of  steam,  when  its  performance  in  an  engine 
cylinder  is  plotted  in  a  curve,  see  Fig.  83. 


166  NOTES   ON  PRACTICAL  MECHANICAL,  DRAWING. 

Let  AO  and  OB  be  two  reference  lines  at  right  angles 
to  each  other,  and  let  P  be  an  assumed  point  of  the  curve. 
Through  P  draw  lines  parallel  to  OA  and  OB,  respectively; 
also,  draw  any  line,  OQ.  From  the  points  in  which  the 
line,  OQ,  cuts  the  parallels  through  P  to  OA  and  OB, 
respectively,  erect  perpendiculars,  and  these  will  intersect 
in  a  point  on  the  curve,  and  so  for  as  many  points  desired. 

To  find  the  point,  0,  given  any  two  points,  as  K  and 
L,  on  the  curve  and  one  of  the  reference  lines:  Draw  a 
parallelogram  upon  K  and  L  as  vertices  similar  to  the  one 
erected  at  P.  A  diagonal  of  the  parallelogram  will  cut  the 
given  reference  lines  in  the  point,  0.  The  latter  con- 
struction is  in  common  use  when  applying  the  hyperbola 
to  indicator  cards  of  engines. 

85.     The  cycloid. 

The  cycloids  belong  to  a  class  of  curves  otherwise 
known  as  roulettes.  A  roulette  is  the  path  traced  by  a 
point  upon  a  curve  which  rolls  upon  another  curve,  the 
latter  being  fixed.  The  rolling  curve  is  the  generatrix,  and 
that  upon  which  it  rolls  is  called  the  directrix.  A  cycloid 
may  be  described  as  a  curve  traced  by  a  point  upon  a 
circle,  which  rolls  on  a  straight  line  or  another  circle; 
although  the  cycloid,  proper,  is  understood  to  be  that 
curve  traced  by  a  point  upon  a  circle  which  rolls  upon  a 
straight  line,  and  the  distinguishing  terms,  epicycloid  and 
hypocycloid,  are  used  to  mean  the  path  of  a  point  upon  a 
circle  which  rolls  upon  the  outside  and  the  inside  of 
another  circle,  respectively. 

The  cycloidal  curves  are  those  used  extensively  for  the 
outlines  of  gear  teeth,  and  every  draftsman  should  at  least 


GEOMETRICAL    DRAWING. 


167 


be  familiar  in  the  beginning  with  their  construction.  The 
aim  in  the  construction  of  gear  teeth  is  to  get  rolling 
contact. 

86.    To  construct  the  cycloid,  see  Fig.  84. 

Let  AB  be  the  fixed  line  or  directrix  upon  which  the 
circle,  EP"C,  rolls.  Suppose  the  circle  to  move  in  the 
direction  of  the  arrow.  When  the  circumference  has 


rolled  a  given  fraction  of  its  length  upon  the  line  AB,  the 
center,  O,  will  have  moved  a  linear  distance  equal  to  this, 
or  to  O',  that  is,  GO'  =  CP'  =  EP".  The  point  P" 
will  lie  on  the  directrix  and  the  point  C  will  have  moved 
the  distance  towards  [the  directrix  that  P"  is  from  it 
originally.  Hence,  draw  a  line  parallel  to  the  directrix 
through  P',  and  with  O'  as  a  center  and  radius  equal  to 
the  given  circle,  describe  an  arc  to  cut  this  parallel  in  the 
point  P,  which  will  be  a  point  of  the  curve.  Repeat  this 
process  for  as  many  points  as  desired. 

The  curve  is  symmetrical  upon  the  vertical  line,  EC. 
The  tangent  to  the  curve  at  C  is  parallel  to  the  directrix 
AB,  the  tangent  at  A  is  perpendicular  to  the  directrix.  If 
the  circle  continued  to  roll  on  AB  it  would  generate 


168  NOTES   ON   PRACTICAL  MECHANICAL  DRAWING. 

another  loop,  and  the  point  A,  would  be  a  cusp  of  the  curve. 
In  gear  design,  only  a  small  portion  of  the  curve,  in  the 
neighborhood  of  A  or  B,  would  be  used  for  the  line  of  the 
tooth. 

87.  To  draw  the  epicycloid: 

The  epicycloid,  and  also  the  hypocycloid,  are  the 
more  common  curves  for  gear  teeth,  the  cycloid  being 
limited  to  the  teeth  on  a  rack.  Let  A  E  B,  with  F  as 
center,  Fig.  85,  be  the  directrix,  and  EDO,  with  O  as 
center,  be  the  generatix.  If  the  circle  EDO  rolls  through 
a  given  circumferential  length  upon  the  directrix  toward 
the  left,  the  center  O  will  travel  a  greater  distance,  pro- 
portional to  its  distance  from  the  center  F.  Assume  the 
circumferential  length  to  be  E  P  or  one-twelfth  of  the  cir- 
cumference. P  will  come  down  to  the  directrix  at  P'  and 
C  will  move  one-twelfth  of  the  circumferential  length  to 
the  left  of  C,  or  to  a  distance  from  the  directrix  that  P' ' 
is.  Hence,  through  P'  draw  a  radius  of  the  directrix  upon 
which  the  new  position  of  the  center  0  will  lie,  or  0',  and 
at  0 '  draw  an  arc  of  the  rolling  circle  in  its  new  position, 
also  with  F  as  a  center,  draw  an  arc  of  a  circle  of  radius 
FP' '.  Where  these  two  arcs  intersect  in  Q,  is  one  point 
in  the  epicycloid.  By  similar  process,  as  many  points  can 
be  plotted  as  desired.  The  curve  is  symmetrical  upon  the 
line  FO.  The  tangent  to  the  curve  at  C  is  normal  to  the 
radius  F  O  C,  and  the  tangent  at  A  is  normal  to  the 
directrix. 

88.  To  draw  the  hypocycloid,  see  Fig.  85. 

The  hypocycloid  is  similarly  constructed  to  the 
epicycloid,  the  generatrix,  or  rolling  circle,  moving  on  the 


GEOMETRICAL   DRAWING 
FIGURE  No.    85. 


169 


inside  of  the  directrix.  The  epicycloid  is  the  curve  of  the 
face  or  upper  half,  the  hypocycloid,  the  flank  or  lower 
half  of  the  tooth  outline.  The  center  R  of  the  generating 
circle  GE.,  it  will  be  seen,  travels  through  a  shorter 
linear  distance  than  the  points  on  the  circumference. 

When  the  circumference  has  rolled  off  a  distance,  for 
example  EP' ' ' ,  the  center  will  have  traveled  to  the  position 
R'  and  the  point  G  will  have  traveled  one-twelfth  of  the 
circumferential  length  to  the  left  or  to  the  distance  from 


170  NOTES   ON   PRACTICAL  MECHANICAL,  DRAWING. 

the  directrix  that  H  is.  Hence,  through  P"  '  draw  a  radius 
of  the  directrix  upon  which  the  new  position  of  the  center 
of  the  generating  circle  will  lie,  and  with  this  point,  R'  ,  as 
center,  describe  an  arc  of  the  generating  circle;  also  with 
F  as  a  center  describe  an  arc  of  a  circle  of  radius  FH. 
Where  these  two  curves  intersect,  is  a  point  in  the 
hypocycloid,  and  so  on  for  as  many  points  as  desired.  If 
the  circumference  of  the  generating  circle  will  go  an  even 
number  of  times  into  that  of  the  directrix,  there  will  be 
that  even  number  of  loops,  or  cusps.  If  the  generatrix 
does  not  go  an  even  number  of  times  into  the  directrix, 
then  the  cusps  will  not  close  entirely. 

Both  epicycloid  and  hypocycloid  have  common  tan- 
gents at  the  points,  A  and  B,  which  tangents  are  radii  of 
the  directrix. 

89.     To  draw  the  involute  of  a  circle. 

The  involute  of  a  circle  may  be  defined  as  the  path 
traced  by  any  point  of  its  circumference  if  the  latter  is 
conceived  to  unroll  from  the  circle  as  a  thread  from  a 
spool.  Or  again,  geometrically,  it  is  the  locus  of  the 
extremities  of  a  series  of  tangents  to  the  circle,  starting  at 
some  fixed  reference  point  and  whose  lengths  are  respec- 
tively equal  to  the  circumferential  lengths  between  the 
points  of  tangency  and  the  reference  point.  It  is  a  curve, 
which  like  the  cycloids,  finds  illustration  in  forms  of  gear 
teeth,  a  gear  which  works  on  a  rack. 

Let  ABC,  Fig.  86,  be  any  circle  with  A  a  fixed 
reference  point.  Divide  the  circle  conveniently  into  a 
number  of  equal  divisions.  Starting  at  the  first  division, 
on  either  side  of  the  reference  point,  draw  a  tangent  and 


GEOMETRICAL,   DRAWING, 
FIGURE  No.  86. 


171 


make  its  length  equal  to  the  length  of  the  arc  between  the 
point  of  tangency  and  the  point  A.  Its  extremity  is  one 
point  on  the  curve  of  the  involute.  Next,  draw  a  tangent 
at  the  second  equal  division  and  make  its  length  equal  to 
two  segments  of  the  circumference,  establishing  by  its 
extremity  another  point  in  the  curve,  and  so  on  for  as 
many  points  as  desired  necessary  to  draw  a  smooth  curve 
through  them. 


9O.    Geometrical  definitions,  terms,  etc. 

Curves,  in  a  mathematical  sense,  include  straight  lines  as  well 
as  curves.  A  straight  line  is  a  curve  of  infinite  radius. 

A  plane  figure  is  a  plane  bounded  on  all  sides  by  lines.  If 
the  lines  are  straight,  the  space  which  they  enclose  is  called 
a  rectilinear  figure,  or  polygon,  and  the  sum  of  the  bounding  lines 
is  the  perimeter  of  the  polygon. 

Polygons  are  named  according  to  the  number  of  their  sides  as  a 
triangle,  quadrilateral,  pentagon,  hexagon;  a  heptagon,  of  seven 


172  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 

sides;  octagon,  of  eight;  nonagon,  or  enneagon,  of  nine;  decagon, 
often;  undecagon,  of  eleven;  dodecagon,  of  twelve.  Polygons  are 
supposed  to  be  regular  unless  otherwise  stated. 

A  diameter  of  a  polygon  is  any  line  drawn  through  the  center  of 
a  figure,  and  terminated  by  the  opposite  boundaries. 

The  long  diameter  of  a  polygon  is  the  diameter  of  its  circum- 
scribed circle.  This  is  also  called  a  diagonal. 

The  short  diameter  of  a  polygon  is  the  diameter  of  its  inscribed 
circle. 

A  polyhedron  is  a  solid  bounded  entirely  by  planes. 

There  are  only  five  regular  polyhedrons,  viz.: 

The  tetrahedron,  bounded  by  four  equilateral  triangles. 

The  hexahedron,  or  cube,  bounded  by  six  equal  squares. 

The  octahedron,  bounded  by  eight  equilateral  triangles. 

The  dodecahedron,  bounded  by  twelve  equal  pentagons. 

The  icosahedron,  bounded  by  twenty  equal  equilateral  triangles. 

A  prism  is  a  polyhedron  having  two  of  its  faces,  called  its  ends 
or  bases,  parallel,  and  the  rest  parallelograms. 

A  parallelopiped  is  a  prism  whose  bases  are  parallelograms. 

The  axis  of  a  prism  is  a  straight  line  joining  the  centers  of  its 
bases. 

The  axis  of  a  pyramid  is  a  straight  line  from  its  vertex  to  the 
center  of  its  base. 

A  right  prism,  or  pyramid,  has  its  axis  at  right  angles  to  its  base. 


CHAPTER  VII. 
MACHINE  SKETCHING. 

91.     Machine  sketching. 

One  of  the  most  important  accomplishments  an  engineer 
can  have  is  the  ability  to  make  a  free-hand  working 
drawing  sketch.  The  machine  designer  finds  it  invaluable 
if  he  can  turn  his  sketches  over  to  the  junior  draftsman  to 
work  up.  The  junior  draftman  finds  it  valuable  if  a  part 
of  a  machine  has  to  be  repaired,  and  temporary  drawings 
made  of  it,  or  again,  to  make  a  record  of  construction  for 
future  reference. 

No  particular  scale  is  in  general  required  in  sketching, 
but  a  proper  proportioning  of  each  view  and  its  size 
relative  to  other  views. 

To  get  the  proper  relation  of  values,  i.e.,  distances  and 
sizes  of  lines,  a  certain  ratio  must  be  obtained.  The  ratio 
in  perspective  drawing  or  picture  making  is  a  very  different 
problem  from  that  in  mechanical  drawing.  In  the  former 
the  ratios  are  between  sizes  that  are  not  of  certain  true 
length,  but  apparent  lengths  due  to  the  obliquity  of  these 
lines  to  the  observer,  or  foreshortening,  as  it  is  called, 
while  in  mechanical  drawing  these  are  absolute  sizes  being 
the  practical  lengths,  as  a  rule,  that  are  in  the  subject.— 

Therefore,  to  obtain  a  value  to  record  in  drawing  that 
is  a  ratio  between  two  quantities,  estimate  the  value  in  the 
original  by  assigning  either  a  numerical  ratio  of  simple 
numbers  easily  transferred,  or  else,  carry  a  conception 


174  NOTES   ON   PRACTICAL  MECHANICAL  DRAWING. 

of  the  ratio  value  in  the  mind  without  assigning  any 
numerical  value.  For  illustration,  if  a  certain  detail  is 
one-fifth  as  long  as  the  over  all  dimension,  then  that  detail 
in  the  drawing  should  be  one-fifth  as  long  as  the  overall. 
In  some  cases  of  rather  large  subjects  it  may  be  advisable 
to  make  a  space  measurement  of  •  sizes  for  comparison. 
For  illustration,  if  a  certain  detail  is  one-fifth  the  length  of 
an  over  all,  a  pencil  may  be  held  up  between  the  eye  and 
subject,  and  covering  one  end  of  the  detail  to  be  measured 
with  the  end  of  the  pencil,  and  the  other  end  by  the  finger 
moved  along  the  pencil,  this  length  may  be  compared  with 
the  over  all  by  noting  that  it  will  go  into  it  five  times. 
Therefore,  as  the  pencil  unit  is  to  the  whole  unit  stepped 
off  with  it,  so  the  detail  in  the  drawing  should  be  to  the 
over  all  in  the  drawing.  This  method  can  be  used  where 
the  quantities  to  be  measured  do  not  extend  throughout  a 
very  wide  range  of  vision,  else  the  foreshortening,  before 
mentioned,  will  cut  a  very  serious  figure  and  introduce 
inaccuracies.  An  eye  estimate  of  values  is  better  than  an 
actual  measurement  made.  After  the  drawing  has  all  been 
made,  however,  its  accuracy  may  be  tested  by  these  means 
very  nicely. 

Sometimes  sketching  may  take  the  form  of  a  hasty  draw- 
ing or  drawings  of  a  model  from  which  afterwards  working 
drawings  can  be  made.  It  is  possible,  generally,  to  get  the 
data  into  two  or  three  views.  The  problem  is  to  choose  the 
fewest  views,  and  some  discrimination  has  to  be  exercised 
to  ascertain  what  they  are.  Or  it  may  be  that  the  final 
drawing  is  to  be  one  which  shows  all  the  constructive  facts 
— without  being  a  working  drawing — with  the  fewest  views. 
Such  a  problem  is  illustrated  by  a  patent  office  drawing. 


MACHINE    SKETCHING.  175 

Sketching  may  be  done  upon  regular  sheets,  but  more 
frequently  it  is  put  upon  scratch  paper,  or  the  pages  of  a 
note  book.  Use  of  a  rule  and  compas  is  here  not  feasible. 
If  done  on  the  pages  of  a  note  book,  the  first  problem  is  to 
adopt  such  a  size  that  the  subject  may  be  treated  properly 
and  legibly.  It  may  involve  only  one  view  on  a  page,  or  it 
may  involve  two  or  more.  If  there  is  room  for  more  than 
one  view  on  a  page  they  should  be  sketched  in  the  same 
protective  relation  to  one  another  that  they  would  be  if 
mechanically  drawn,  and  upon  the  different  sheets  of  the 
note  book,  as  far  as  possible,  the  views  should  be  sketched 
in  the  same  position  that  they  would  occupy,  if  drawn 
mechanically  on  a  sheet;  otherwise,  a  little  confusion  in 
reading  the  sketches  may  result.  Where  several  views  are 
to  go  on  one  page,  in  the  sketching  they  should  be  roughly 
blocked  out  for  proper  allotment  of  space  before  doing 
further  work  upon  any  one  view;  where  feasible,  sketch 
them  together  throughout. 

In  very  rare  cases  a  whole  view  even  cannot  be  put  on  a 
sheet.  It  should  be  stopped  at  a  conventional  line,  such  as 
was  described  in  the  case  of  sections  where  the  plane  of 
the  section  moved  from  one  place  to  another,  and  it  is 
furthermore  best  to  sketch  the  two  or  more  parts  on  the 
sheet  in  the  same  relative  position  so  that,  if  called  for, 
they  may  be  cut  along  the  line  of  their  separation  and 
fastened  together  to  make  the  complete  view. 

Views  of  parts  should  be  sketched  as  occupying  the 
relative  position  which  they  would  in  the  machine. 

Some  further  practical  points  about  sketching  follow :  — 

(a.)  Throughout  sketching,  observe,  carefully,  right 
angles  and  the  rounded  corners;  the  latter  may,  in  the 


176  NOTES   ON  PRACTICAL  MECHANICAL  DRAWING. 

preliminary  operations,  be  made  sharp,  and  only  in  the 
final  stage  rounded  off  to  the  desired  amount.  Be  sure 
that  the  right  angles  are  always  as  near  right  angles  as 
they  can  be  made. 

(&.)  Where  forms  are  symmetrical  upon  a  center  or 
center  line,  sketch  the  two  or  more  parts  at  the  same  time. 
The  brief  preliminary  record  made  upon  one  side  should 
be  followed  by  the  same  record  on  the  other  side,  and  as 
each  stage  is  gone  through  with  on  the  one,  it  should  be 
followed  by  the  same  stage  on  the  other.  The  mistake  is 
quite  common  to  draw  one  side  of  a  thing  that  is  symmetri- 
cal on  an  axis  and  then  copy  it  faithfully  on  the  other. 

(c.)  Sketches  of  a  subject,  if  made  from  a  model  or  the 
original,  should  be  finished  complete  before  any  dimensions 
are  put  on,  for  the  problem  of  sketching  does  not  involve 
scale  or  absolute  size;  it  is  better  if  these  are  not  con- 
sidered. And  it  is  to  be  observed  that  the  lines  of  the 
sketches  should  be  much  sharper  and  blacker  if  they  are 
to  be  dimensioned,  than  if  left  without,  for  dimension 
lines  and  figures  cover  up  form.  When  sketches  are  ready 
for  dimensions  these  should  be  taken  from  the  subject  in 
the  way  heretofore  described  for  mechanical  drawings, 
noting  in  particular  to  take  only  one  dimension  at  a  time. 

(d.)  Sometimes  sketches  must  ~be  made  hurriedly,  when 
it  is  very  important  to  subdivide  the  time  to  be  used  into 
parts  to  be  given  each  to  certain  stages  of  the  drawing. 
Eoughly  speaking,  about  as  much  time  should  be  allowed 
for  dimensioning  as  that  for  making  sketches.  Again, 
the  time  alloted  for  sketching  may  be  divided  in  parts, 
three  of  which  to  be  given  to  the  light  perliminary 
work,  and  one  part  to  finishing  up  in  clear  line,  for  the 


MACHINE  SKETCHING.  177 

proportioning  and  the  shape  are  more  important  than  the 
character  of  the  line. 

(e.)  If  time  has  been  improperly  allotted,  or  a  great 
deal  has  to  be  accomplished  in  a  very  short  time,  it  may 
be  desirable  to  cut  steps  short  by  leaving  out  certain 
things.  Where  parts  are  duplicated,  for  example,  they 
need  not  be  drawn  but  once.  Where  forms  are  encoun- 
tered which  are  perfectly  understood,  like  wheels,  only  a 
small  portion  needs  to  be  sketched.  Much  can  frequently 
be  omitted  by  giving  a  few  written  directions  explanatory 
of  them;  this  is  true  of  holes  for  bolts,  fastenings  of  a 
similar  character,  etc.  Where  forms  are  symmetrical  upon 
a  center  line  only  one-half  need  be  sketched;  where 
symmetrical  upon  a  center  perhaps  only  one-quarter,  a 
note  being  used  to  refer  to  the  ommitted  parts. 

(/.)  A  complicated  subject  may  have  to  be  drawn  in  a 
very  compact  space,  and  in  short  time.  There  may  not  be 
room  upon  the  pages  of  the  note  book  to  develop  the 
forms,  either  entire  or  in  separate  parts,  and  even  proper 
proportioning  is  not  feasible.  It  may  be  necessary  to 
sketch  neglecting  proportions  entirely,  or  it  may  be 
convenient  to  change  one  dimension  without  changing  the 
other.  Again,  it  may  be  that  some  parts  can  be  shown  in 
proportion,  while  others  are  not,  compressing  the  drawing 
where  needed  to  make  it  fit  the  space.  These  are 
practical  problems  that  can  easily  be  solved  when  they 
arise.  With  a  knowledge  of  the  principles  of  sketching,  it 
becomes  merely  the  question  of  recognizing  the  limiting 
conditions  of  the  particular  problem  in  hand.  The  drafts- 
man who  expects  to  do  comprehensive  work  caimot  afford 
to  be  without  a  knowledge  of  sketching. 


APPENDIX. 


BLUE  PRINT  PROCESS  AND  REPRODUCTION. 

A  mechanical  drawing  made  to  be  worked  from  is 
generally  reproduced  by  blue  print,  or  analogous  process. 
A  drawing  may  be  reproduced  in  photo  engraving  to 
furnish  a  cut  for  a  catalogue. 

The  following  upon  the  subject  of  blue  prints  is  taken 
from  F.  N.  Willson's  'Theoretical  and  Practical  Graphics:' 

"A  sheet  of  paper  may  be  sensitized  to  the  action  of 
light  by  coating  its  surface  with  a  solution  of  red  prussiate 
of  potash  (ferrocyanide  of  potassium)  and  a  ferric  salt. 
The  chemical  action  of  light  upon  this  is  the  production  of 
a  ferrous  salt  from  the  ferric  compound;  this  combines 
with  the  ferrocyanide  to  produce  the  final  blue  undertone 
of  the  sheet;  while  the  portions  of  the  paper,  from  which 
the  light  was  intercepted  by  the  inked  lines,  becomes  white 
after  immersion  in  water." 

44 The  proportions  in  which  the  chemicals  are  to  be 
mixed  are,  apparently,  a  matter  of  indifference,  so  great  is 
the  disparity  between  the  receipts  of  different  writers." 

44 The  entire  process,  while  exceedingly  simple  in  theory, 
varies,  as  to  its  result,  with  the  experience  and  judgment 
of  the  manipulator.  To  his  choice  the  decision  is  left 
between  the  following  standard  recipes  for  preparing  the 
sensitizing  solution.  The  "parts"  given  are  all  by  weight. 
In  every  case  the  potash  should  be  pulverized,  to  facilitate 
its  dissolving." 


180  NOTES   ON   PRACTICAL  MECHANICAL  DRAWING. 

No.  1.     FROM  LE  GENIE  CIVIL. 

SOLUTION. 

No.  1.  Red  Prussiate  of  Potash 8  parts 

Water 70  parts 

No.  2.  Citric  of  Iron  and  Ammonia 10  parts 

Water 70  parts 

Filter    the    solutions    separately,    mix    equal 
quantities,  and  then  filter  again. 

No.  1.     FROM   THE    U.  S.  LABORATORY,  WILLETT'S 

POINT. 

SOLUTION. 

No.  1.  Double  Citrate  of  Iron  and  Ammonia,  1  ounce 
Water 4  ounces 

No.  2.  Red  Prussiate  of  Pocassium 1  ounce 

Water 4  ounces 

"The  solutions  should  be  dissolved  separately,  as  then 
they  are  not  sensitive  to  the  action  of  light.  They  should 
be  mixed  and  applied  only  in  the  dark  room." 

"The  best  American  practice  is  to  apply  the  solution 
with  a  flat  brush,  and  to  obtain  an  even  coat  by  stroking 
first  one  way,  then  at  right  angles.  If  necessary,  a  coat  of 
diagonal  strokes  may  be  given  to  secure  evenness." 

"To  copy  a  drawing,  it  is  placed  in  a  blue  print  frame 
made  for  the  purpose,  the  sensitized  paper,  with  the 
sensitized  surface  outermost  and  immediately  back  of  the 
drawing.  Exposure  for  about  five  minutes  to  the  rays  of 
the  sun  is  usually  sufficient  to  get  good  results,  after  which 
the  paper  is  taken  out  and  placed  in  a  bath  of  water  when 
the  superfluous  chemicals  are  washed  off." 

"White  lines  can  be  drawn  upon  a  blue  print  by  using 
a  solution  of  soda,  potash,  quick  lime,  or  any  alkali  with 
water,  adding  a  little  gum  arabic  to  keep  the  liquid  from 
spreading.  It  can  be  applied  with  the  writing  pen,  ruling 
pen  or  brush,  according  to  the  area  desired  to  be  white." 


INDEX 


Alternator,  convention  for.__  102 

Ammeter,  convention  for 102 

Angles,  and  how  to  dimension,    99 

Appendix 179 

Arc  lamps,  convention  for___  102 
Arrangement  of  working 

drawings 71 

Arrow  heads  in  dimensioning  96 
Ascending  small  Roman 

letters__  7 

Assembly  drawing  defined. __  67 
Auxiliary  plane  of  projection  27 

Axes,  isometric 40 

Axes  of  prism  and  pyramid 

defined 172 

Babbit,  standard  section  for__    86 

Beam  compass 47 

Bed  of  engine,  problem  18 140 

Bell,  convention  for  electric..  102 
Bench  grinder,  problems  16 

and  17 140 

Bench  vise,  problem  24 147 

Bill  of  materials 18,  68 

Blue  print  process 179 

Boards,  dimensioning  of 99 

Bolts 98,  114 

Bolts,  names  of 118 

Bolts,  table  of  sizes,  etc 116 

Bow  instruments 47 

Bow  instruments,  handling  of    63 

Bracket,  problem  13 139 

Brake  shoe,  problem  12 135 

Brass,  color  convention  for__  J03 
Brass,  standard  sectioning  for  86 
Brick,  color  convention  for___  103 

Cap  bolt  defined 118 

Care  and  handling  of  instru- 
ments     48 

Cast   iron,    color  convention 

for__  _  103 


Page 

Cast  iron,   standard   section- 
ing for 86 

Center  of  projection 20 

Checking  of  drawings 101 

Circle  defined 157 

Circle,  to  draw  the  involute  of  170 

Circle,  the  projection  of 27 

Civil  engineers'  scale 77 

Civil  engineers'  scale,  use  of    80 

Cleaning  of  drawings 48,  60 

Cloth,  tracing 46 

Colors     as    conventions    for 

materials 103 

Color,  how  to  put  on  a  draw- 
ing   104 

Compass,  beam  compass 47 

Compass,  handling  of 60 

Condenser,  convention  for___  102 

Conies  defined 157 

Conventional  colors  for  ma- 
terials   103 

Conventional    threads    for 

screws 111 

Conventions    on    working 

drawings 102 

Coordinate  planes  of  projec- 
tion    ___    21 

Crank;  overhung,  Problem  9,  133 
Crossed  wires,  convention  for  102 

Cube,  projection  of 26 

Curves,    how    to    draw   with 

compass 62 

Curve,  use  of  irregular 64 

Curves  in  isometric  drawing.    42 

Curves,  projection  of 31 

Curve,  tangent  to 154 

Cycloid,  the 166 

Cylinder    head    and    stuffing 

box,  problem  15 140 

Decimals  for  dimensions.-         94 


182 


INDEX 


Page 

Definitions,  geometrical 171 

Detail  drawing  defined 68 

Development    of    working 

drawings 71 

Diagram  drawing  defined 67 

Diameter  of  a  polygon  defined  172 

Difference  between  first   and 
third  angle 32 

Dimensioning  discussed 91 

Dimension  figures 96 

Dimensions,  inking  of 94 

Dimensioning      of     standard 

bolts 115 

Dimensioning,  system  in 93 

Dimension,    what    to   dimen- 
sion and  how  to  place___    97 
Discharge  cap  for  pump,  prob- 
lem 11 135 

Dividers,     also    the    propor- 
tional      47 

Dividers,  handling  of 63 

Dodecahedron  defined 172 

Dotted  lines 56 

Dotting  wheels 47 

Drafting    machine,    the   Uni- 
versal and  Paragon 48 

Drawing  boards 44 

Drawings,  checking  of 101 

Drawings,  cleaning  of 48,  60 

Drawings,      conventions     on 

working  drawings 102 

Drawings,    development    and 

arrangement  of 71 

Drawings,  directions  for  pen- 
ciling     54 

Drawings,  errors  in  and  how 

to  correct 52 

Drawing,  isometric,  defined.-    39 
Drawing,  mechanical,  defined    20 

Drawing  to  scale 77 

Drawing  as  a  science 19 

Drawings,  symbols  for 100 

Drawing,  of  what  a   working 
drawing  consists 67 


Page 
Drawing,  working  drawing 

defined 20 

Driving  wheel,  locomotive 

problem   23 147 

Earth,  color  convention  for__  103 

Ellipse,  to  draw 158 

End  projection  of  figures 27 

Engine  bed,  problem  18 140 

Engineer's  scale 77 

Engineer's  scale,  use  of 80 

Epicycloid,  to  draw 168 

Erasures,  method  of 56 

Errors  in  drawings  and  how 

to   correct 52 

Face,  'spot' 100 

Fastening  of  paper  to  board__    54 

Feet,    convention    for    in   di- 
mensioning      96 

Figures  for  dimensioning 96 

Figures,  projection  of  plane__    25 
Fillets,  and  how  to  dimension    99 

Finish,  notes  for 100 

First    and    third    angle    dis- 
cussed     32 

Fixed  end  casting,  problem  20,  147 

Flat  scale 77 

Flywheel,  problem  22 147 

Follower  pens 47 

French  curve, see  'curve' 

Geometrical  definitions 171 

Geometrical  drawing 153 

Glass,  standard  sectioning  for    86 

Gothic  letter 9 

Gothic,  Roman-Gothic  letter.     15 

Grind  defined 100 

Grinder,  bench,  problems   16 

and  17 140 

Ground  line  defined 21 

Handling  of  instruments 48 

Height  of  letters  vary 2 

Helix 106 

Hexagonal  bolts _  114 


INDEX 


183 


Page 
Hexagonal  bolt  head,  drawing 

of —  116 

Hexahedron  defined 172 

Horizontal   coordinate   plane 

defined 22 

Hyperbola  defined 158 

Hyperbola,  to  draw 163 

Hypocycloid,  to  draw 168 

Icosahedron  defined 172 

Involute  of  a  circle,  to  draw.  170 

I  beams,  sectioning  of 89 

Incandescent    light,    conven- 
tion for 102 

Inches,  convention  for 96 

Inclined  Gothic  letter. 9 

Inlet  pipe  flange,  Problem  4_.  126 

Inking  of  dimensions 94 

Inking,  directions  for  inking 

a  drawing 57 

Inking,  system  of 59 

Inking  on  tracing  cloth 106 

Instruments,  the  bows 47 

Instruments,  care  and  hand- 
ling of 44,  48 

Irregular  curve,  see  'curve'.. 
Irregular  curve,  tangent  to...  154 

Isometric  axes 40 

Isometric  drawing  defined    39,  42 
Joined  wires,  convention  for.  102 
Lines,  limiting  lines  for  di- 
mension lines 95 

Lever  stop,  problem  8 133 

Lead,  standard  sectioning  for    86 
Lead  pencil,  sharpening  and 

use  of 55 

Lettering 1 

Lettering,  the  off-hand 9 

Letters,      ascending    small 

Roman 7 

Letters,  the  Gothic 9 

Letters,  the  old  Roman 13 

Letters,  short,  small  Roman.      7 

Letters,  the  stump 18 

Letters,  the  Roman-Gothic..    15 


Page 

Letters,  vary  in  height 2 

Letters,  vary  in  width... 2 

Lines,  ground  line  defined. ._    21 


Lines,  dimensioning  lines  and 
treatment  of._ 


95 


Lines,  dotted 56 

Lines,  limiting 95 

Liners,  mechanical  section 88 

Lines,  projection  of 24 

Lines,    the    proper    way    to 
draw    with    the    ruling 
pen ..  50 
Line,  right  line  pen,  see  'rul- 
ing'  

Lines,  weight  of 58 

Lining,  standard  section 85 

Locomotive     driving    wheel, 

problem  23 147 

Machine  bolt  defined 118 

Machine  sketching 173 

Machine,     the    Universal 

Drafting 48 

Masonry,     color    convention 

for 103 

Materials,  bill  of,  defined..  18,  68 
Mechanical  drawing  defined..    20 

Mechanical  section  liners 88 

Motor,  convention  for 102 

Notes  on  drawings 97 

Notes  for  finish 100 

Numerals,  Roman,  discussed      7 
Oblique  projection  defined    39,  42 

Octahedron  defined 172 

Off-hand  lettering 9 

Off-hand  lettering,    handling 

of  and  styles 11 

Off-hand  lettering,  the  pen  for    13 

Orthographic  projection 19 

Orthographic  projection, 
rules  violated  in  sec- 
tions    89 

Orthographic   projection  and 

working  drawings 66 

Outlet  pipe  flange,  problem  4,  126 


184 


INDEX 


Page 

Overall  dimensions 92 

Overhung  crank,  problem  9__  133 
Packing,  standard  sectioning 

for 86 

Paper,  drawing 45 

Paper,  how  to  fasten  to 

board 54 

Paper,  stretching  of 46 

Parabola  defined 158 

Parabola,  to  draw 162 

Paragon  drafting  machine 48 

Parallel  lines,  how  to  draw__.  353 

Parallel  straight  edge 48 

Parallelepiped  defined 172 

Pen,  use  of  ruling  pen  and 

difficulties  with 50,  57 

Pen,  follower 47 

Pen  for  off-hand  lettering 13 

Pen,  ruling,  the  handling  of  __  49 

Pen,  to  sharpen  ruling  pen 51 

Penciling,  directions  for 54 

Penciling,  system  in 57 

Perpendicular  defined 153 

Pile,  Standard  Pile  Bridge 

problem  19 140 

Pillow  block,  problem  14 139 

Piston  head,  problem  21 147 

Plan,  sectional 82 

Plane,  arbitrary  plane  of  pro- 
jection    27 

Planes,  coordinate  planes  of 

projection 21 

Plane  figure,  projection  of___  25 

Plane  finish 100 

Plates,  iron,  dimensions  of__  99 

Point,  projection  of 22 

Polish  defined 100 

Polygon  defined 172 

Polyhedron  defined 172 

Powell  thread  for  screws 114 

Primary  battery,  convention 

for 102 

Prism,  axis  of,  defined 172 

Prism  defined..  .  172 


Page 

Problems  in  projection _  33 

Problems  in  us©  of  scale 78 

Problems    in  working   draw- 
ings  123-152 

Profile  projection 27 

Projection,  center  of___ _  20 

Projection  of  a  circle 27 

Projection,  coordinate  planes 

of 21 

Projection  of  a  cube 26 

Projection   of  curves  in  gen- 
eral   31 

Projection,  end   projection  of 

a  figure 27 

Projection  of  helix 107 

Projection,  isometric,  defined  39 

Projection  of  lines 24 

Projection,  oblique,  defined..  42 
Projection,  orthographic,  de- 
fined   19 

Projection  of  plane  figure 25 

Projection  of  a  point 22 

Projection,  problems  in 33 

Projection,  profile 27 

Projection,  rules  violated  in 


Projection  of  a  solid 26 

Projection  and  working  draw- 
ings __.          66 

Proportional  dividers 47 

Proportions   of  bolts,  heads, 

etc 114 

Proportion  in  sketching 173 

Protractor 48 

Pyramid,  axis  of,  defined 172 

Bail,  standard,  100  lb.,  prob- 
lem 7 130 

Rectify  an  arc  of  a  circle 155 

Reproduction,  process  of 179 

Resistance,  convention  for__  102 

Rheostat,  convention  for 102 

Right  angle,  to  divide 154 

Right  line  pen 49 

Right  prism  or  pyramid 172 


INDEX 


185 


Page 
Rivet  defined. 121 

Rivets,  to  dimension 99 

Rocker  arm,  problem  10 135 

Rod,  convention  for  round...  103 

Roman-Gothic  letter 15 

Roman  letter  discussed 3 

Roman  numerals  discussed  __  7 
Roman,  the  old  Roman  letter  13 

Roman  small  letters 7 

Rules   of  projection  violated 

69,  89 

Ruling,  directions  for  lines...    55 

Ruling  pen 49 

Scale  drawing 77 

Scale,  handling  of 78 

Scale  in  sketching. 173 

Scrape,  defined 100 

Screws,     convention    for 

threads 1 Ill 

Screws,  forms  of  thread 113 

Screws,  names  of 118 

Screw,  the  V  threaded.. 108 

Sections  defined 68,  80 

Section  liners,  mechanical 88 

Section  lining,  standardized..  85 
Sectional  plan  and  elevation  82 
Sectioning,  practical  points 

about 87 

Sections,  violate  rules  of  pro- 
jection        89 

Sellers  standard  threads 113 

Set  screws  defined 119 

Shaft,  convention  for  break  in  103 
Sharpening  of  a  ruling  pen___  51 
Short  small  Roman  letters.. _  7 

Size  of  plate  for  drawings 54 

Sketching,   machine 173 

Sketching,    practical    points 

about 173 

Solid,  the  projection  of 26 

Special  scale 80 

Spot  face  defined 100 

Spurs  on  Roman  letters 5 


Page 

Square  bolts 114 

Standard  bolts,  dimensioning 

of 115 

Standard    Pile  Bridge,   prob- 
lem 19 ___  140 

Standard  100-lb.  rail,  problem 

7 130 

Standard  threads  for  screws. _  112 
Standardized  section  lining...  85 
Steel,  color  convention  for...  103 
Steel,  standard  sectioning  for  86 
Stone,  color  convention  for__  103 
Stop  lever,  problem  8 133 

Storage  battery,    convention 

for 102 

Straight  edge,  the  parallel 48 

Strength,    uniform    strength 

bolts 121 

Stretching  of  paper 46 

Stud  bolt  defined... 118 

Stump  letter 18 

Stuffing  box,  problem  15 140 

Switch,  convention  for 102 

System  of  dimensioning 93 

Symbols  on  drawings 100 

System  of  inking 59 

System  in  penciling 57 

Table  of  bolts  sizes,  etc 116 

Tangency  defined 154 

Tangent  to  two  oblique  lines  156 
Tangent  to  an  irregular  curve  154 

Tap  bolt  defined 118 

Taper  and  how  to  dimension.    99 
Tapped  hole   and  how  to  di- 
mension  98 

Tee  bar  in  section.. 102 

Tee  square,  use  of 45,  54 

Tetrahedron  defined 172 

Third    and    first    angle    dis- 
cussed     32 

Treads,      convention     for 

screws 111 

Threads,  forms  of  screw...    _  113 


186 


INDEX 


Page 

Tint  of  color,  how  to  put  on__  104 
Titles  to  drawings  discussed.    15 

Tracings 106 

Tracing  cloth 46 

Triangles,  use  of,  etc 45,  55 

Triangular  connected  circuit, 

convention  for 102 

Triangular  scale__ 77 

Trim,  defined 100 

Tri-phase  circuit,  convention 

for 102 

Uniform  strength  bolt. 121 

Uniformity  in  lettering 1 

U.  S.  Standard  threads 113 

Units  in  division  of  letters...      5 
Universal  drafting  machine..    48 
Variable   resistance,  conven- 
tion for 102 

Variations     in     width    and 

height  of  letters 2 

Vertical  coordinate  plane* 22 


Vertical  defined 153 

Vise,  bench,  problem  24 147 

Volt  meter,  convention  for__.  102 

V  threaded  screws. __ _  108 

Weight  of  lines 58 

Whitworth  standard  thread..  112 

Width  of  letters  varies 2 

Witness  lines 95 

Wood,  color  convention  for__  103 
Wood,     standard    sectioning 

for i 86 

Working  drawings 66 

Working    drawings,    conven- 
tions    _  102 

Working  drawings  defined---    20 
Working  drawings,    develop- 
ment and  arrangement.    71 
Wrought  iron   color   conven- 
tion for. 103 

Wrought  iron,  standard,  sec- 
tioning for... _    86 


UNIVERSITY 

OF 


YC   19720 


